| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 576.1-a1 |
576.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$82.74177487$ |
1.379029581 |
\( -\frac{112296627634165}{21} a^{3} + \frac{162833319690280}{7} a^{2} - \frac{361939789578460}{21} a - \frac{47784088225037}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{16}{7} a^{3} - \frac{31}{7} a^{2} - \frac{152}{7} a - \frac{95}{7}\) , \( \frac{82}{7} a^{3} - \frac{32}{7} a^{2} - \frac{464}{7} a - \frac{59}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}^{2}+\left(\frac{16}{7}a^{3}-\frac{31}{7}a^{2}-\frac{152}{7}a-\frac{95}{7}\right){x}+\frac{82}{7}a^{3}-\frac{32}{7}a^{2}-\frac{464}{7}a-\frac{59}{7}$ |
| 576.1-a2 |
576.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$82.74177487$ |
1.379029581 |
\( 347838 a^{3} - \frac{4542100}{3} a^{2} + \frac{3366730}{3} a + \frac{446522}{3} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{4}{7} a^{3} - \frac{1}{7} a^{2} + \frac{38}{7} a + \frac{15}{7}\) , \( \frac{8}{7} a^{3} - \frac{12}{7} a^{2} - \frac{48}{7} a + \frac{19}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}^{2}+\left(-\frac{4}{7}a^{3}-\frac{1}{7}a^{2}+\frac{38}{7}a+\frac{15}{7}\right){x}+\frac{8}{7}a^{3}-\frac{12}{7}a^{2}-\frac{48}{7}a+\frac{19}{7}$ |
| 576.1-b1 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$137.4703049$ |
2.291171749 |
\( \frac{17924871210986965706}{21} a^{3} - \frac{12631159738955468836}{7} a^{2} - \frac{121153604521133693882}{21} a + \frac{52404172759077623448}{7} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{187}{7} a^{3} - \frac{697}{7} a^{2} + \frac{390}{7} a + \frac{25}{7}\) , \( -\frac{2284}{7} a^{3} + \frac{8732}{7} a^{2} - \frac{5896}{7} a - \frac{787}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}^{2}+\left(\frac{187}{7}a^{3}-\frac{697}{7}a^{2}+\frac{390}{7}a+\frac{25}{7}\right){x}-\frac{2284}{7}a^{3}+\frac{8732}{7}a^{2}-\frac{5896}{7}a-\frac{787}{7}$ |
| 576.1-b2 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$549.8812199$ |
2.291171749 |
\( \frac{11288992}{3} a^{3} + 5062288 a^{2} - \frac{28033984}{3} a - 1071552 \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{9}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{20}{7} a^{3} + \frac{37}{7} a^{2} + \frac{148}{7} a - \frac{156}{7}\) , \( \frac{5}{7} a^{3} - \frac{11}{7} a^{2} - \frac{30}{7} a + \frac{32}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{20}{7}a-\frac{9}{7}\right){x}^{2}+\left(-\frac{20}{7}a^{3}+\frac{37}{7}a^{2}+\frac{148}{7}a-\frac{156}{7}\right){x}+\frac{5}{7}a^{3}-\frac{11}{7}a^{2}-\frac{30}{7}a+\frac{32}{7}$ |
| 576.1-b3 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$34.36757624$ |
2.291171749 |
\( \frac{13093229065272928}{21} a^{3} + \frac{17676969495774340}{21} a^{2} - \frac{10811085568081144}{7} a - \frac{3908327657755916}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{9}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -4 a^{2} + 14 a - 3\) , \( \frac{127}{7} a^{3} - \frac{376}{7} a^{2} - \frac{356}{7} a + \frac{635}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{20}{7}a-\frac{9}{7}\right){x}^{2}+\left(-4a^{2}+14a-3\right){x}+\frac{127}{7}a^{3}-\frac{376}{7}a^{2}-\frac{356}{7}a+\frac{635}{7}$ |
| 576.1-b4 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$137.4703049$ |
2.291171749 |
\( -\frac{5271885790650650}{189} a^{3} + \frac{68799450670862180}{567} a^{2} - \frac{50974941397685090}{567} a - \frac{6729824157140584}{567} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{2}{7}\) , \( 0\) , \( -\frac{129}{7} a^{3} - \frac{20}{7} a^{2} + \frac{662}{7} a - \frac{1}{7}\) , \( -\frac{1776}{7} a^{3} + \frac{2769}{7} a^{2} + \frac{17166}{7} a + \frac{1998}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{2}{7}\right){x}^{2}+\left(-\frac{129}{7}a^{3}-\frac{20}{7}a^{2}+\frac{662}{7}a-\frac{1}{7}\right){x}-\frac{1776}{7}a^{3}+\frac{2769}{7}a^{2}+\frac{17166}{7}a+\frac{1998}{7}$ |
| 576.1-b5 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$549.8812199$ |
2.291171749 |
\( \frac{896271200}{3} a^{3} - \frac{5668221460}{9} a^{2} - \frac{18244966520}{9} a + 2626945708 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{19}{7}\) , \( 0\) , \( -\frac{66}{7} a^{3} - \frac{230}{7} a^{2} + \frac{298}{7} a + \frac{48}{7}\) , \( -\frac{794}{7} a^{3} - \frac{566}{7} a^{2} + \frac{1460}{7} a + \frac{174}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{19}{7}\right){x}^{2}+\left(-\frac{66}{7}a^{3}-\frac{230}{7}a^{2}+\frac{298}{7}a+\frac{48}{7}\right){x}-\frac{794}{7}a^{3}-\frac{566}{7}a^{2}+\frac{1460}{7}a+\frac{174}{7}$ |
| 576.1-b6 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$137.4703049$ |
2.291171749 |
\( -\frac{13184512}{21} a^{3} + \frac{11662592}{21} a^{2} + \frac{35092480}{7} a + \frac{11880704}{21} \) |
\( \bigl[0\) , \( \frac{3}{7} a^{3} - \frac{8}{7} a^{2} - \frac{18}{7} a + \frac{36}{7}\) , \( 0\) , \( \frac{8}{7} a^{3} - \frac{12}{7} a^{2} - \frac{62}{7} a + \frac{26}{7}\) , \( \frac{4}{7} a^{3} + \frac{1}{7} a^{2} - \frac{38}{7} a - \frac{43}{7}\bigr] \) |
${y}^2={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{8}{7}a^{2}-\frac{18}{7}a+\frac{36}{7}\right){x}^{2}+\left(\frac{8}{7}a^{3}-\frac{12}{7}a^{2}-\frac{62}{7}a+\frac{26}{7}\right){x}+\frac{4}{7}a^{3}+\frac{1}{7}a^{2}-\frac{38}{7}a-\frac{43}{7}$ |
| 576.1-c1 |
576.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.058244049$ |
$393.8674081$ |
3.058724395 |
\( \frac{3880}{7} a^{3} - \frac{5820}{7} a^{2} - \frac{23280}{7} a + \frac{380}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{16}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{17}{7} a^{3} - \frac{57}{7} a^{2} + \frac{52}{7} a + \frac{22}{7}\) , \( -\frac{65}{7} a^{3} + \frac{178}{7} a^{2} - \frac{114}{7} a - \frac{10}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{16}{7}\right){x}^{2}+\left(\frac{17}{7}a^{3}-\frac{57}{7}a^{2}+\frac{52}{7}a+\frac{22}{7}\right){x}-\frac{65}{7}a^{3}+\frac{178}{7}a^{2}-\frac{114}{7}a-\frac{10}{7}$ |
| 576.1-c2 |
576.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.116488099$ |
$393.8674081$ |
3.058724395 |
\( -\frac{58130540}{21} a^{3} + \frac{29065270}{7} a^{2} + \frac{116261080}{7} a + \frac{116011960}{63} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{16}{7}\) , \( 0\) , \( -3 a^{3} - 13 a^{2} - 17 a - 2\) , \( -\frac{426}{7} a^{3} - \frac{495}{7} a^{2} + \frac{1254}{7} a + \frac{138}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{16}{7}\right){x}^{2}+\left(-3a^{3}-13a^{2}-17a-2\right){x}-\frac{426}{7}a^{3}-\frac{495}{7}a^{2}+\frac{1254}{7}a+\frac{138}{7}$ |
| 576.1-d1 |
576.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$3.354119112$ |
0.894431763 |
\( \frac{24470537412833990}{189} a^{3} - \frac{155193382970687210}{567} a^{2} - \frac{496186629834540100}{567} a + \frac{214622172993436232}{189} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{19}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{327}{7} a^{3} - \frac{277}{7} a^{2} - \frac{2522}{7} a - \frac{213}{7}\) , \( \frac{1289}{7} a^{3} - \frac{2280}{7} a^{2} - \frac{13019}{7} a - \frac{1437}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{19}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{327}{7}a^{3}-\frac{277}{7}a^{2}-\frac{2522}{7}a-\frac{213}{7}\right){x}+\frac{1289}{7}a^{3}-\frac{2280}{7}a^{2}-\frac{13019}{7}a-\frac{1437}{7}$ |
| 576.1-d2 |
576.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$53.66590579$ |
0.894431763 |
\( -\frac{425927920}{7} a^{3} + \frac{17195034340}{63} a^{2} - \frac{14674501600}{63} a + \frac{308619184}{63} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{4}{7} a^{3} - \frac{6}{7} a^{2} - \frac{31}{7} a + \frac{27}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{327}{7} a^{3} - \frac{172}{7} a^{2} - \frac{2725}{7} a - \frac{1235}{7}\) , \( -\frac{4737}{7} a^{3} + \frac{5289}{7} a^{2} + \frac{36752}{7} a - \frac{4379}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(\frac{4}{7}a^{3}-\frac{6}{7}a^{2}-\frac{31}{7}a+\frac{27}{7}\right){x}^{2}+\left(\frac{327}{7}a^{3}-\frac{172}{7}a^{2}-\frac{2725}{7}a-\frac{1235}{7}\right){x}-\frac{4737}{7}a^{3}+\frac{5289}{7}a^{2}+\frac{36752}{7}a-\frac{4379}{7}$ |
| 576.1-d3 |
576.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$214.6636231$ |
0.894431763 |
\( -\frac{60774903797317424}{21} a^{3} + \frac{53845542602292404}{21} a^{2} + \frac{485409166658666144}{21} a + \frac{18184915096098432}{7} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{47}{7} a^{3} + \frac{102}{7} a^{2} + \frac{324}{7} a - \frac{438}{7}\) , \( \frac{121}{7} a^{3} - \frac{290}{7} a^{2} - \frac{656}{7} a + \frac{927}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(-\frac{47}{7}a^{3}+\frac{102}{7}a^{2}+\frac{324}{7}a-\frac{438}{7}\right){x}+\frac{121}{7}a^{3}-\frac{290}{7}a^{2}-\frac{656}{7}a+\frac{927}{7}$ |
| 576.1-d4 |
576.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$858.6544927$ |
0.894431763 |
\( -\frac{122101408}{7} a^{3} + \frac{108204624}{7} a^{2} + \frac{2925410048}{21} a + \frac{328923824}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -a^{3} + a^{2} + 12 a - 14\) , \( -2 a^{3} + a^{2} + 28 a - 30\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(-a^{3}+a^{2}+12a-14\right){x}-2a^{3}+a^{2}+28a-30$ |
| 576.1-d5 |
576.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$3.354119112$ |
0.894431763 |
\( -\frac{1287233326405587122}{7} a^{3} + \frac{5599574123070366666}{7} a^{2} - \frac{12446522180683247348}{21} a - \frac{1643217294016906232}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{4}{7} a^{3} - \frac{6}{7} a^{2} - \frac{31}{7} a + \frac{13}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{824}{7} a^{3} + \frac{1656}{7} a^{2} + \frac{5623}{7} a - \frac{6598}{7}\) , \( -\frac{12476}{7} a^{3} + \frac{25322}{7} a^{2} + \frac{85349}{7} a - \frac{101279}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{4}{7}a^{3}-\frac{6}{7}a^{2}-\frac{31}{7}a+\frac{13}{7}\right){x}^{2}+\left(-\frac{824}{7}a^{3}+\frac{1656}{7}a^{2}+\frac{5623}{7}a-\frac{6598}{7}\right){x}-\frac{12476}{7}a^{3}+\frac{25322}{7}a^{2}+\frac{85349}{7}a-\frac{101279}{7}$ |
| 576.1-d6 |
576.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$858.6544927$ |
0.894431763 |
\( \frac{2866688}{21} a^{3} + \frac{3814144}{21} a^{2} - \frac{7258112}{21} a - \frac{288768}{7} \) |
\( \bigl[0\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{26}{7}\) , \( 0\) , \( \frac{2}{7} a^{3} - \frac{10}{7} a^{2} - \frac{12}{7} a + \frac{31}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a + \frac{12}{7}\bigr] \) |
${y}^2={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}+\frac{1}{7}a+\frac{26}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}-\frac{10}{7}a^{2}-\frac{12}{7}a+\frac{31}{7}\right){x}+\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a+\frac{12}{7}$ |
| 576.1-e1 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{16} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.311730320$ |
$516.8363050$ |
5.370451569 |
\( \frac{1556068}{81} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{19}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{46}{7} a^{3} + \frac{69}{7} a^{2} + \frac{437}{7} a - \frac{538}{7}\) , \( \frac{136}{7} a^{3} - \frac{204}{7} a^{2} - \frac{1292}{7} a + \frac{1492}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{19}{7}a+\frac{10}{7}\right){x}^{2}+\left(-\frac{46}{7}a^{3}+\frac{69}{7}a^{2}+\frac{437}{7}a-\frac{538}{7}\right){x}+\frac{136}{7}a^{3}-\frac{204}{7}a^{2}-\frac{1292}{7}a+\frac{1492}{7}$ |
| 576.1-e2 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$4.987685129$ |
$2.018891816$ |
5.370451569 |
\( \frac{22730892706564}{3} a^{3} - 11365446353282 a^{2} - \frac{215943480712358}{3} a + \frac{251453177267660}{3} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 0\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{110}{7} a^{3} - \frac{165}{7} a^{2} - \frac{1045}{7} a - \frac{248}{7}\) , \( \frac{922}{7} a^{3} - \frac{1383}{7} a^{2} - \frac{8759}{7} a - \frac{1200}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{110}{7}a^{3}-\frac{165}{7}a^{2}-\frac{1045}{7}a-\frac{248}{7}\right){x}+\frac{922}{7}a^{3}-\frac{1383}{7}a^{2}-\frac{8759}{7}a-\frac{1200}{7}$ |
| 576.1-e3 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.311730320$ |
$516.8363050$ |
5.370451569 |
\( \frac{3065617154}{9} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} + \frac{5373}{7} a^{2} - \frac{5395}{7} a - \frac{42340}{7}\) , \( \frac{1}{7} a^{3} - \frac{152808}{7} a^{2} + \frac{152797}{7} a + \frac{1203046}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{26}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}+\frac{5373}{7}a^{2}-\frac{5395}{7}a-\frac{42340}{7}\right){x}+\frac{1}{7}a^{3}-\frac{152808}{7}a^{2}+\frac{152797}{7}a+\frac{1203046}{7}$ |
| 576.1-e4 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$4.987685129$ |
$2.018891816$ |
5.370451569 |
\( -\frac{22730892706564}{3} a^{3} + 11365446353282 a^{2} + \frac{215943480712358}{3} a + \frac{24144250202020}{3} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{19}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{106}{7} a^{3} + \frac{159}{7} a^{2} + \frac{1007}{7} a - \frac{1328}{7}\) , \( -\frac{920}{7} a^{3} + \frac{1380}{7} a^{2} + \frac{8740}{7} a - \frac{10410}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{19}{7}a+\frac{10}{7}\right){x}^{2}+\left(-\frac{106}{7}a^{3}+\frac{159}{7}a^{2}+\frac{1007}{7}a-\frac{1328}{7}\right){x}-\frac{920}{7}a^{3}+\frac{1380}{7}a^{2}+\frac{8740}{7}a-\frac{10410}{7}$ |
| 576.1-e5 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{32} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.246921282$ |
$32.30226906$ |
5.370451569 |
\( \frac{207646}{6561} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} - \frac{227}{7} a^{2} + \frac{205}{7} a + \frac{1760}{7}\) , \( \frac{1}{7} a^{3} - \frac{9924}{7} a^{2} + \frac{9913}{7} a + \frac{78118}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{26}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}-\frac{227}{7}a^{2}+\frac{205}{7}a+\frac{1760}{7}\right){x}+\frac{1}{7}a^{3}-\frac{9924}{7}a^{2}+\frac{9913}{7}a+\frac{78118}{7}$ |
| 576.1-e6 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.246921282$ |
$32.30226906$ |
5.370451569 |
\( \frac{28756228}{3} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} + \frac{893}{7} a^{2} - \frac{915}{7} a - \frac{7060}{7}\) , \( \frac{1}{7} a^{3} + \frac{12126}{7} a^{2} - \frac{12137}{7} a - \frac{95482}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{26}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}+\frac{893}{7}a^{2}-\frac{915}{7}a-\frac{7060}{7}\right){x}+\frac{1}{7}a^{3}+\frac{12126}{7}a^{2}-\frac{12137}{7}a-\frac{95482}{7}$ |
| 576.1-e7 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.311730320$ |
$516.8363050$ |
5.370451569 |
\( \frac{35152}{9} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} + \frac{53}{7} a^{2} - \frac{75}{7} a - \frac{445}{7}\) , \( \frac{1}{7} a^{3} + \frac{219}{7} a^{2} - \frac{230}{7} a - \frac{1738}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{26}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}+\frac{53}{7}a^{2}-\frac{75}{7}a-\frac{445}{7}\right){x}+\frac{1}{7}a^{3}+\frac{219}{7}a^{2}-\frac{230}{7}a-\frac{1738}{7}$ |
| 576.1-e8 |
576.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.311730320$ |
$129.2090762$ |
5.370451569 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}$ |
| 576.1-f1 |
576.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$3.354119112$ |
0.894431763 |
\( \frac{5271885790650650}{189} a^{3} + \frac{21352478555006330}{567} a^{2} - \frac{39176987828183420}{567} a - \frac{4720972255915444}{567} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{129}{7} a^{3} - \frac{414}{7} a^{2} - \frac{221}{7} a + \frac{519}{7}\) , \( -247 a^{3} + 363 a^{2} + 2381 a - 2767\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{9}{7}\right){x}^{2}+\left(\frac{129}{7}a^{3}-\frac{414}{7}a^{2}-\frac{221}{7}a+\frac{519}{7}\right){x}-247a^{3}+363a^{2}+2381a-2767$ |
| 576.1-f2 |
576.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$53.66590579$ |
0.894431763 |
\( -\frac{896271200}{3} a^{3} + \frac{2398219340}{9} a^{2} + \frac{21514968640}{9} a + 268681888 \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{3}{7} a^{3} - \frac{1}{7} a^{2} - \frac{25}{7} a + \frac{8}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{75}{7} a^{3} - \frac{445}{7} a^{2} + \frac{292}{7} a + \frac{123}{7}\) , \( -\frac{816}{7} a^{3} + \frac{2694}{7} a^{2} - \frac{1838}{7} a - \frac{181}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{1}{7}a^{2}-\frac{25}{7}a+\frac{8}{7}\right){x}^{2}+\left(\frac{75}{7}a^{3}-\frac{445}{7}a^{2}+\frac{292}{7}a+\frac{123}{7}\right){x}-\frac{816}{7}a^{3}+\frac{2694}{7}a^{2}-\frac{1838}{7}a-\frac{181}{7}$ |
| 576.1-f3 |
576.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$858.6544927$ |
0.894431763 |
\( -\frac{11288992}{3} a^{3} + 16351280 a^{2} - \frac{36206720}{3} a - 1590928 \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{9}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{9}{7} a^{3} - \frac{17}{7} a^{2} - \frac{68}{7} a - \frac{18}{7}\) , \( \frac{39}{7} a^{3} - \frac{48}{7} a^{2} - \frac{332}{7} a - \frac{43}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{9}{7}\right){x}^{2}+\left(\frac{9}{7}a^{3}-\frac{17}{7}a^{2}-\frac{68}{7}a-\frac{18}{7}\right){x}+\frac{39}{7}a^{3}-\frac{48}{7}a^{2}-\frac{332}{7}a-\frac{43}{7}$ |
| 576.1-f4 |
576.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$214.6636231$ |
0.894431763 |
\( -\frac{13093229065272928}{21} a^{3} + \frac{56956656691593124}{21} a^{2} - \frac{42200369483124032}{21} a - \frac{1857128600317360}{7} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{9}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{11}{7} a^{3} - \frac{22}{7} a^{2} + \frac{52}{7} a + \frac{22}{7}\) , \( \frac{96}{7} a^{3} - \frac{39}{7} a^{2} - \frac{632}{7} a - \frac{52}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{9}{7}\right){x}^{2}+\left(-\frac{11}{7}a^{3}-\frac{22}{7}a^{2}+\frac{52}{7}a+\frac{22}{7}\right){x}+\frac{96}{7}a^{3}-\frac{39}{7}a^{2}-\frac{632}{7}a-\frac{52}{7}$ |
| 576.1-f5 |
576.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$3.354119112$ |
0.894431763 |
\( -\frac{17924871210986965706}{21} a^{3} + \frac{5293711472031496870}{7} a^{2} + \frac{143165949321905609780}{21} a + \frac{5363435250073245220}{7} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{3}{7} a^{3} - \frac{8}{7} a^{2} - \frac{18}{7} a + \frac{22}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{186}{7} a^{3} - \frac{141}{7} a^{2} + \frac{430}{7} a - \frac{90}{7}\) , \( -\frac{2475}{7} a^{3} - \frac{2010}{7} a^{2} + \frac{5183}{7} a + \frac{106}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{8}{7}a^{2}-\frac{18}{7}a+\frac{22}{7}\right){x}^{2}+\left(-\frac{186}{7}a^{3}-\frac{141}{7}a^{2}+\frac{430}{7}a-\frac{90}{7}\right){x}-\frac{2475}{7}a^{3}-\frac{2010}{7}a^{2}+\frac{5183}{7}a+\frac{106}{7}$ |
| 576.1-f6 |
576.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$858.6544927$ |
0.894431763 |
\( \frac{13184512}{21} a^{3} - \frac{27890944}{21} a^{2} - \frac{89049088}{21} a + \frac{38545408}{7} \) |
\( \bigl[0\) , \( \frac{3}{7} a^{3} - \frac{1}{7} a^{2} - \frac{25}{7} a + \frac{8}{7}\) , \( 0\) , \( -\frac{2}{7} a^{3} + \frac{10}{7} a^{2} + \frac{12}{7} a - \frac{45}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{13}{7} a + \frac{30}{7}\bigr] \) |
${y}^2={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{1}{7}a^{2}-\frac{25}{7}a+\frac{8}{7}\right){x}^{2}+\left(-\frac{2}{7}a^{3}+\frac{10}{7}a^{2}+\frac{12}{7}a-\frac{45}{7}\right){x}-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{13}{7}a+\frac{30}{7}$ |
| 576.1-g1 |
576.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$82.74177487$ |
1.379029581 |
\( \frac{112296627634165}{21} a^{3} + \frac{50536692056115}{7} a^{2} - \frac{278170245660725}{21} a - \frac{33520546366822}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{2}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{20}{7} a^{3} + \frac{23}{7} a^{2} + \frac{204}{7} a - \frac{282}{7}\) , \( -\frac{85}{7} a^{3} + \frac{222}{7} a^{2} + \frac{307}{7} a - \frac{502}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{2}{7}\right){x}^{2}+\left(-\frac{20}{7}a^{3}+\frac{23}{7}a^{2}+\frac{204}{7}a-\frac{282}{7}\right){x}-\frac{85}{7}a^{3}+\frac{222}{7}a^{2}+\frac{307}{7}a-\frac{502}{7}$ |
| 576.1-g2 |
576.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$82.74177487$ |
1.379029581 |
\( -347838 a^{3} - \frac{1411558}{3} a^{2} + \frac{2586928}{3} a + \frac{314666}{3} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{2}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -a^{2} + 2 a + 4\) , \( -\frac{11}{7} a^{3} + \frac{20}{7} a^{2} + \frac{73}{7} a - \frac{62}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{20}{7}a+\frac{2}{7}\right){x}^{2}+\left(-a^{2}+2a+4\right){x}-\frac{11}{7}a^{3}+\frac{20}{7}a^{2}+\frac{73}{7}a-\frac{62}{7}$ |
| 576.1-h1 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$6.410817304$ |
1.709551281 |
\( -\frac{1648843669531189209612}{7} a^{3} + \frac{21517829335001719685821}{21} a^{2} - \frac{15943006509814183965871}{21} a - \frac{2104830862418857027849}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{9}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{292}{7} a^{3} - \frac{654}{7} a^{2} - \frac{26}{7} a - \frac{389}{7}\) , \( -\frac{5665}{7} a^{3} - \frac{10322}{7} a^{2} + \frac{7740}{7} a + \frac{1411}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{9}{7}\right){x}^{2}+\left(-\frac{292}{7}a^{3}-\frac{654}{7}a^{2}-\frac{26}{7}a-\frac{389}{7}\right){x}-\frac{5665}{7}a^{3}-\frac{10322}{7}a^{2}+\frac{7740}{7}a+\frac{1411}{7}$ |
| 576.1-h2 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$102.5730768$ |
1.709551281 |
\( \frac{7653445524629136161292}{7} a^{3} - \frac{48538537682942480968381}{21} a^{2} - \frac{155188146360477304157009}{21} a + \frac{201376751357535261279001}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{6}{7} a - \frac{9}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1934}{7} a^{3} - \frac{1802}{7} a^{2} - \frac{15573}{7} a - \frac{1915}{7}\) , \( -\frac{35030}{7} a^{3} + \frac{31223}{7} a^{2} + \frac{281202}{7} a + \frac{31833}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{6}{7}a-\frac{9}{7}\right){x}^{2}+\left(\frac{1934}{7}a^{3}-\frac{1802}{7}a^{2}-\frac{15573}{7}a-\frac{1915}{7}\right){x}-\frac{35030}{7}a^{3}+\frac{31223}{7}a^{2}+\frac{281202}{7}a+\frac{31833}{7}$ |
| 576.1-h3 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$102.5730768$ |
1.709551281 |
\( \frac{58879180820}{7} a^{3} - \frac{88318771230}{7} a^{2} - \frac{559352217790}{7} a + \frac{1953996095168}{21} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{16}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( 7 a^{3} - 11 a^{2} - 68 a - 16\) , \( \frac{447}{7} a^{3} - \frac{254}{7} a^{2} - \frac{3186}{7} a - \frac{369}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{16}{7}\right){x}^{2}+\left(7a^{3}-11a^{2}-68a-16\right){x}+\frac{447}{7}a^{3}-\frac{254}{7}a^{2}-\frac{3186}{7}a-\frac{369}{7}$ |
| 576.1-h4 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$102.5730768$ |
1.709551281 |
\( -\frac{78880}{3} a^{3} + 39440 a^{2} + \frac{749360}{3} a - \frac{2616068}{9} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{16}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{11}{7} a^{3} + \frac{13}{7} a^{2} + \frac{94}{7} a + \frac{8}{7}\) , \( \frac{9}{7} a^{3} + \frac{4}{7} a^{2} - \frac{54}{7} a - \frac{39}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{16}{7}\right){x}^{2}+\left(-\frac{11}{7}a^{3}+\frac{13}{7}a^{2}+\frac{94}{7}a+\frac{8}{7}\right){x}+\frac{9}{7}a^{3}+\frac{4}{7}a^{2}-\frac{54}{7}a-\frac{39}{7}$ |
| 576.1-i1 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.267131810$ |
$231.4783872$ |
4.122349385 |
\( \frac{396031132}{27} a^{3} - \frac{198015566}{9} a^{2} - \frac{792062264}{9} a + \frac{8510605768}{81} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{3}{7} a^{3} - \frac{1}{7} a^{2} - \frac{32}{7} a + \frac{1}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{446}{7} a^{3} - \frac{452}{7} a^{2} - \frac{3691}{7} a - \frac{374}{7}\) , \( \frac{677}{7} a^{3} - \frac{354}{7} a^{2} - \frac{4769}{7} a - \frac{507}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(\frac{3}{7}a^{3}-\frac{1}{7}a^{2}-\frac{32}{7}a+\frac{1}{7}\right){x}^{2}+\left(\frac{446}{7}a^{3}-\frac{452}{7}a^{2}-\frac{3691}{7}a-\frac{374}{7}\right){x}+\frac{677}{7}a^{3}-\frac{354}{7}a^{2}-\frac{4769}{7}a-\frac{507}{7}$ |
| 576.1-i2 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1.068527243$ |
$14.46739920$ |
4.122349385 |
\( -\frac{1532318514980}{21} a^{3} + \frac{766159257490}{7} a^{2} + \frac{3064637029960}{7} a + \frac{1016109581608}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{6}{7} a - \frac{9}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 3 a^{3} - 64 a^{2} + 241 a - 197\) , \( \frac{1992}{7} a^{3} - \frac{10380}{7} a^{2} + \frac{14088}{7} a - \frac{5601}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{6}{7}a-\frac{9}{7}\right){x}^{2}+\left(3a^{3}-64a^{2}+241a-197\right){x}+\frac{1992}{7}a^{3}-\frac{10380}{7}a^{2}+\frac{14088}{7}a-\frac{5601}{7}$ |
| 576.1-i3 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.534263621$ |
$231.4783872$ |
4.122349385 |
\( -\frac{285560}{3} a^{3} + 142780 a^{2} + 571120 a + \frac{671372}{9} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{6}{7} a - \frac{9}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{39}{7} a^{3} + \frac{62}{7} a^{2} + \frac{367}{7} a - \frac{419}{7}\) , \( \frac{204}{7} a^{3} - \frac{558}{7} a^{2} - \frac{804}{7} a + \frac{1293}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{6}{7}a-\frac{9}{7}\right){x}^{2}+\left(-\frac{39}{7}a^{3}+\frac{62}{7}a^{2}+\frac{367}{7}a-\frac{419}{7}\right){x}+\frac{204}{7}a^{3}-\frac{558}{7}a^{2}-\frac{804}{7}a+\frac{1293}{7}$ |
| 576.1-i4 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.068527243$ |
$231.4783872$ |
4.122349385 |
\( \frac{1184}{21} a^{3} - \frac{592}{7} a^{2} - \frac{2368}{7} a + \frac{1664}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{6}{7} a - \frac{9}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a + \frac{26}{7}\) , \( \frac{12}{7} a^{3} - \frac{25}{7} a^{2} - \frac{72}{7} a + \frac{81}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{6}{7}a-\frac{9}{7}\right){x}^{2}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a+\frac{26}{7}\right){x}+\frac{12}{7}a^{3}-\frac{25}{7}a^{2}-\frac{72}{7}a+\frac{81}{7}$ |
| 576.1-j1 |
576.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$82.74177487$ |
1.379029581 |
\( \frac{521247792070655}{21} a^{3} - \frac{367308901908525}{7} a^{2} - \frac{3523096272568195}{21} a + \frac{4571675416772368}{21} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{20}{7} a^{3} - \frac{23}{7} a^{2} - \frac{190}{7} a - \frac{138}{7}\) , \( -\frac{150}{7} a^{3} + \frac{134}{7} a^{2} + \frac{1110}{7} a - \frac{85}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{20}{7}a^{3}-\frac{23}{7}a^{2}-\frac{190}{7}a-\frac{138}{7}\right){x}-\frac{150}{7}a^{3}+\frac{134}{7}a^{2}+\frac{1110}{7}a-\frac{85}{7}$ |
| 576.1-j2 |
576.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$82.74177487$ |
1.379029581 |
\( -\frac{11302846}{7} a^{3} + \frac{71700610}{21} a^{2} + \frac{229170320}{21} a - \frac{99173154}{7} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( a^{2} - 4\) , \( -\frac{8}{7} a^{3} + \frac{12}{7} a^{2} + \frac{48}{7} a - \frac{33}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(a^{2}-4\right){x}-\frac{8}{7}a^{3}+\frac{12}{7}a^{2}+\frac{48}{7}a-\frac{33}{7}$ |
| 576.1-k1 |
576.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1.068527243$ |
$14.46739920$ |
4.122349385 |
\( \frac{1532318514980}{21} a^{3} - \frac{766159257490}{7} a^{2} - \frac{3064637029960}{7} a + \frac{10976179928978}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( 0\) , \( -\frac{3083}{7} a^{3} + \frac{7421}{7} a^{2} + \frac{19933}{7} a - \frac{34154}{7}\) , \( -\frac{102498}{7} a^{3} + \frac{226085}{7} a^{2} + \frac{683378}{7} a - \frac{972999}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}^{2}+\left(-\frac{3083}{7}a^{3}+\frac{7421}{7}a^{2}+\frac{19933}{7}a-\frac{34154}{7}\right){x}-\frac{102498}{7}a^{3}+\frac{226085}{7}a^{2}+\frac{683378}{7}a-\frac{972999}{7}$ |
| 576.1-k2 |
576.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.534263621$ |
$231.4783872$ |
4.122349385 |
\( \frac{285560}{3} a^{3} - 142780 a^{2} - 571120 a + \frac{6239792}{9} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{16}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{40}{7} a^{3} - \frac{67}{7} a^{2} - \frac{373}{7} a + \frac{4}{7}\) , \( -\frac{115}{7} a^{3} + \frac{36}{7} a^{2} + \frac{781}{7} a + \frac{139}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{16}{7}\right){x}^{2}+\left(\frac{40}{7}a^{3}-\frac{67}{7}a^{2}-\frac{373}{7}a+\frac{4}{7}\right){x}-\frac{115}{7}a^{3}+\frac{36}{7}a^{2}+\frac{781}{7}a+\frac{139}{7}$ |
| 576.1-k3 |
576.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.068527243$ |
$231.4783872$ |
4.122349385 |
\( -\frac{1184}{21} a^{3} + \frac{592}{7} a^{2} + \frac{2368}{7} a - \frac{6032}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{16}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -a^{2} + a + 7\) , \( -\frac{8}{7} a^{3} - \frac{2}{7} a^{2} + \frac{69}{7} a + \frac{65}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){y}={x}^{3}+\left(-\frac{1}{7}a^{3}-\frac{2}{7}a^{2}+\frac{6}{7}a+\frac{16}{7}\right){x}^{2}+\left(-a^{2}+a+7\right){x}-\frac{8}{7}a^{3}-\frac{2}{7}a^{2}+\frac{69}{7}a+\frac{65}{7}$ |
| 576.1-k4 |
576.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.267131810$ |
$231.4783872$ |
4.122349385 |
\( -\frac{396031132}{27} a^{3} + \frac{198015566}{9} a^{2} + \frac{792062264}{9} a + \frac{787998694}{81} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{3}{7} a^{3} + \frac{1}{7} a^{2} + \frac{32}{7} a - \frac{1}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{2}{7} a^{3} - \frac{221}{7} a^{2} - \frac{548}{7} a - \frac{87}{7}\) , \( -\frac{634}{7} a^{3} - \frac{99}{7} a^{2} + \frac{3433}{7} a + \frac{386}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{1}{7}a^{2}+\frac{32}{7}a-\frac{1}{7}\right){x}^{2}+\left(-\frac{2}{7}a^{3}-\frac{221}{7}a^{2}-\frac{548}{7}a-\frac{87}{7}\right){x}-\frac{634}{7}a^{3}-\frac{99}{7}a^{2}+\frac{3433}{7}a+\frac{386}{7}$ |
| 576.1-l1 |
576.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.058244049$ |
$393.8674081$ |
3.058724395 |
\( -\frac{3880}{7} a^{3} + \frac{5820}{7} a^{2} + \frac{23280}{7} a - \frac{75280}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{17}{7} a^{3} + \frac{36}{7} a^{2} + \frac{109}{7} a - \frac{120}{7}\) , \( \frac{18}{7} a^{3} - \frac{41}{7} a^{2} - \frac{108}{7} a + \frac{139}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}^{2}+\left(-\frac{17}{7}a^{3}+\frac{36}{7}a^{2}+\frac{109}{7}a-\frac{120}{7}\right){x}+\frac{18}{7}a^{3}-\frac{41}{7}a^{2}-\frac{108}{7}a+\frac{139}{7}$ |
| 576.1-l2 |
576.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.116488099$ |
$393.8674081$ |
3.058724395 |
\( \frac{58130540}{21} a^{3} - \frac{29065270}{7} a^{2} - \frac{116261080}{7} a + \frac{1249557490}{63} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{3}{7} a^{3} + \frac{1}{7} a^{2} + \frac{25}{7} a - \frac{8}{7}\) , \( 0\) , \( a^{3} - 19 a^{2} + 67 a - 48\) , \( \frac{390}{7} a^{3} - \frac{1383}{7} a^{2} - \frac{142}{7} a + \frac{1334}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}={x}^{3}+\left(-\frac{3}{7}a^{3}+\frac{1}{7}a^{2}+\frac{25}{7}a-\frac{8}{7}\right){x}^{2}+\left(a^{3}-19a^{2}+67a-48\right){x}+\frac{390}{7}a^{3}-\frac{1383}{7}a^{2}-\frac{142}{7}a+\frac{1334}{7}$ |
| 576.1-m1 |
576.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.329038312$ |
$100.5267377$ |
4.410286414 |
\( -\frac{3880}{7} a^{3} + \frac{5820}{7} a^{2} + \frac{23280}{7} a - \frac{75280}{21} \) |
\( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( a\) , \( 0\) , \( -\frac{2}{7} a^{3} - \frac{11}{7} a^{2} + \frac{5}{7} a + \frac{53}{7}\) , \( -\frac{18}{7} a^{3} - \frac{15}{7} a^{2} + \frac{80}{7} a + \frac{36}{7}\bigr] \) |
${y}^2+\left(-\frac{3}{7}a^{3}+\frac{8}{7}a^{2}+\frac{18}{7}a-\frac{29}{7}\right){x}{y}={x}^{3}+a{x}^{2}+\left(-\frac{2}{7}a^{3}-\frac{11}{7}a^{2}+\frac{5}{7}a+\frac{53}{7}\right){x}-\frac{18}{7}a^{3}-\frac{15}{7}a^{2}+\frac{80}{7}a+\frac{36}{7}$ |
| 576.1-m2 |
576.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$11.86705$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.658076624$ |
$100.5267377$ |
4.410286414 |
\( \frac{58130540}{21} a^{3} - \frac{29065270}{7} a^{2} - \frac{116261080}{7} a + \frac{1249557490}{63} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{5}{7} a^{3} + \frac{4}{7} a^{2} + \frac{44}{7} a - \frac{18}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{181}{7} a^{3} - \frac{1045}{7} a^{2} + \frac{902}{7} a + \frac{135}{7}\) , \( -\frac{3453}{7} a^{3} + \frac{13618}{7} a^{2} - \frac{9676}{7} a - \frac{1298}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}-\frac{1}{7}a-\frac{12}{7}\right){y}={x}^{3}+\left(-\frac{5}{7}a^{3}+\frac{4}{7}a^{2}+\frac{44}{7}a-\frac{18}{7}\right){x}^{2}+\left(\frac{181}{7}a^{3}-\frac{1045}{7}a^{2}+\frac{902}{7}a+\frac{135}{7}\right){x}-\frac{3453}{7}a^{3}+\frac{13618}{7}a^{2}-\frac{9676}{7}a-\frac{1298}{7}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
