| 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 |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.068789810$ |
$942.8701559$ |
1.430732181 |
\( -128 a^{3} + 192 a^{2} + 1792 a + 640 \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( \frac{1}{9} a^{3} - \frac{2}{3} a^{2} - \frac{5}{9} a + \frac{32}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{32}{9}\) , \( -\frac{5}{9} a^{3} - \frac{2}{3} a^{2} + \frac{34}{9} a + \frac{38}{9}\) , \( -\frac{5}{9} a^{3} - \frac{2}{3} a^{2} + \frac{34}{9} a + \frac{11}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{32}{9}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}-\frac{2}{3}a^{2}-\frac{5}{9}a+\frac{32}{9}\right){x}^{2}+\left(-\frac{5}{9}a^{3}-\frac{2}{3}a^{2}+\frac{34}{9}a+\frac{38}{9}\right){x}-\frac{5}{9}a^{3}-\frac{2}{3}a^{2}+\frac{34}{9}a+\frac{11}{9}$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.034394905$ |
$1885.740311$ |
1.430732181 |
\( -\frac{14368}{9} a^{3} + \frac{7184}{3} a^{2} + \frac{201152}{9} a + \frac{82384}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{17}{3}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{4}{9} a^{3} - \frac{5}{3} a^{2} - \frac{56}{9} a + \frac{56}{9}\) , \( -\frac{2}{3} a^{3} + 2 a^{2} + \frac{25}{3} a - \frac{37}{3}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{17}{3}\right){x}^{2}+\left(\frac{4}{9}a^{3}-\frac{5}{3}a^{2}-\frac{56}{9}a+\frac{56}{9}\right){x}-\frac{2}{3}a^{3}+2a^{2}+\frac{25}{3}a-\frac{37}{3}$ |
| 4.1-b1 |
4.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.068789810$ |
$942.8701559$ |
1.430732181 |
\( -128 a^{3} + 192 a^{2} + 1792 a + 640 \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{32}{9}\) , \( \frac{8}{9} a^{3} - \frac{1}{3} a^{2} - \frac{112}{9} a - \frac{32}{9}\) , \( \frac{8}{9} a^{3} - \frac{1}{3} a^{2} - \frac{112}{9} a - \frac{59}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{32}{9}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}^{2}+\left(\frac{8}{9}a^{3}-\frac{1}{3}a^{2}-\frac{112}{9}a-\frac{32}{9}\right){x}+\frac{8}{9}a^{3}-\frac{1}{3}a^{2}-\frac{112}{9}a-\frac{59}{9}$ |
| 4.1-b2 |
4.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.034394905$ |
$1885.740311$ |
1.430732181 |
\( -\frac{14368}{9} a^{3} + \frac{7184}{3} a^{2} + \frac{201152}{9} a + \frac{82384}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( -\frac{1}{9} a^{3} - \frac{1}{3} a^{2} + \frac{23}{9} a + \frac{13}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( a^{3} - 14 a - 6\) , \( -\frac{14}{9} a^{3} + \frac{4}{3} a^{2} + \frac{169}{9} a - \frac{43}{9}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}-\frac{1}{3}a^{2}+\frac{23}{9}a+\frac{13}{9}\right){x}^{2}+\left(a^{3}-14a-6\right){x}-\frac{14}{9}a^{3}+\frac{4}{3}a^{2}+\frac{169}{9}a-\frac{43}{9}$ |
| 4.2-a1 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( \frac{653762688677050897}{288} a^{3} - \frac{653762688677050897}{192} a^{2} - \frac{4576338820739356279}{144} a + \frac{10804727886792322055}{288} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{23}{9}\) , \( \frac{1}{3} a^{3} - \frac{14}{3} a - \frac{4}{3}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( -\frac{27752}{9} a^{3} + \frac{20350}{3} a^{2} + \frac{295432}{9} a - \frac{395539}{9}\) , \( \frac{2464016}{9} a^{3} - \frac{1757401}{3} a^{2} - \frac{26345266}{9} a + \frac{33230662}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{23}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{14}{3}a-\frac{4}{3}\right){x}^{2}+\left(-\frac{27752}{9}a^{3}+\frac{20350}{3}a^{2}+\frac{295432}{9}a-\frac{395539}{9}\right){x}+\frac{2464016}{9}a^{3}-\frac{1757401}{3}a^{2}-\frac{26345266}{9}a+\frac{33230662}{9}$ |
| 4.2-a2 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$560.4334995$ |
1.030208638 |
\( \frac{67954182989}{6144} a^{3} - \frac{67954182989}{4096} a^{2} - \frac{475679280923}{3072} a + \frac{1123170616927}{6144} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{23}{9}\) , \( \frac{5}{9} a^{3} - \frac{1}{3} a^{2} - \frac{61}{9} a - \frac{2}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( \frac{239}{9} a^{3} - \frac{592}{3} a^{2} + \frac{1775}{9} a + \frac{97}{9}\) , \( -\frac{5729}{9} a^{3} + \frac{10792}{3} a^{2} - \frac{25904}{9} a - \frac{4372}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{23}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){y}={x}^{3}+\left(\frac{5}{9}a^{3}-\frac{1}{3}a^{2}-\frac{61}{9}a-\frac{2}{9}\right){x}^{2}+\left(\frac{239}{9}a^{3}-\frac{592}{3}a^{2}+\frac{1775}{9}a+\frac{97}{9}\right){x}-\frac{5729}{9}a^{3}+\frac{10792}{3}a^{2}-\frac{25904}{9}a-\frac{4372}{9}$ |
| 4.2-a3 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( -\frac{54503407609}{18} a^{3} + \frac{54503407609}{12} a^{2} + \frac{381523853263}{9} a + \frac{55242005306}{9} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{23}{9}\) , \( \frac{1}{3} a^{3} - \frac{14}{3} a - \frac{4}{3}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( \frac{256}{3} a^{3} - 20 a^{2} - \frac{3236}{3} a - \frac{2278}{3}\) , \( \frac{20159}{9} a^{3} - \frac{7126}{3} a^{2} - \frac{237307}{9} a + \frac{14512}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{23}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{14}{3}a-\frac{4}{3}\right){x}^{2}+\left(\frac{256}{3}a^{3}-20a^{2}-\frac{3236}{3}a-\frac{2278}{3}\right){x}+\frac{20159}{9}a^{3}-\frac{7126}{3}a^{2}-\frac{237307}{9}a+\frac{14512}{9}$ |
| 4.2-a4 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( \frac{55573026649}{75497472} a^{3} - \frac{55573026649}{50331648} a^{2} - \frac{389011186543}{37748736} a - \frac{215919499889}{150994944} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{23}{9}\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{19}{9} a + \frac{1}{9}\) , \( 0\) , \( \frac{401}{9} a^{3} - \frac{226}{3} a^{2} - \frac{4471}{9} a + \frac{3319}{9}\) , \( \frac{10136}{9} a^{3} - \frac{7672}{3} a^{2} - \frac{107056}{9} a + \frac{152461}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{23}{9}\right){x}{y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{19}{9}a+\frac{1}{9}\right){x}^{2}+\left(\frac{401}{9}a^{3}-\frac{226}{3}a^{2}-\frac{4471}{9}a+\frac{3319}{9}\right){x}+\frac{10136}{9}a^{3}-\frac{7672}{3}a^{2}-\frac{107056}{9}a+\frac{152461}{9}$ |
| 4.2-a5 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( -\frac{653762688677050897}{288} a^{3} + \frac{653762688677050897}{192} a^{2} + \frac{4576338820739356279}{144} a + \frac{2650337801950168097}{576} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{17}{3}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{27746}{9} a^{3} - \frac{7399}{3} a^{2} - \frac{334228}{9} a - \frac{66830}{9}\) , \( -\frac{821338}{3} a^{3} + 235538 a^{2} + \frac{9832532}{3} a + \frac{1359076}{3}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{17}{3}\right){x}^{2}+\left(\frac{27746}{9}a^{3}-\frac{7399}{3}a^{2}-\frac{334228}{9}a-\frac{66830}{9}\right){x}-\frac{821338}{3}a^{3}+235538a^{2}+\frac{9832532}{3}a+\frac{1359076}{3}$ |
| 4.2-a6 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( \frac{54503407609}{18} a^{3} - \frac{54503407609}{12} a^{2} - \frac{381523853263}{9} a + \frac{1801566841885}{36} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{5}{9} a - \frac{31}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{32}{9}\) , \( \frac{152}{9} a^{3} - \frac{394}{3} a^{2} + \frac{968}{9} a + \frac{175}{9}\) , \( \frac{3980}{9} a^{3} - \frac{5755}{3} a^{2} + \frac{12680}{9} a + \frac{2215}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{32}{9}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{5}{9}a-\frac{31}{9}\right){x}^{2}+\left(\frac{152}{9}a^{3}-\frac{394}{3}a^{2}+\frac{968}{9}a+\frac{175}{9}\right){x}+\frac{3980}{9}a^{3}-\frac{5755}{3}a^{2}+\frac{12680}{9}a+\frac{2215}{9}$ |
| 4.2-a7 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$560.4334995$ |
1.030208638 |
\( -\frac{67954182989}{6144} a^{3} + \frac{67954182989}{4096} a^{2} + \frac{475679280923}{3072} a + \frac{275669927173}{12288} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{17}{3}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{1426}{9} a^{3} - \frac{239}{3} a^{2} - \frac{17588}{9} a - \frac{8350}{9}\) , \( -\frac{33446}{9} a^{3} + \frac{7630}{3} a^{2} + \frac{406252}{9} a + \frac{124892}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{17}{3}\right){x}^{2}+\left(\frac{1426}{9}a^{3}-\frac{239}{3}a^{2}-\frac{17588}{9}a-\frac{8350}{9}\right){x}-\frac{33446}{9}a^{3}+\frac{7630}{3}a^{2}+\frac{406252}{9}a+\frac{124892}{9}$ |
| 4.2-a8 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$560.4334995$ |
1.030208638 |
\( -\frac{101773}{8} a^{3} + \frac{305319}{16} a^{2} + \frac{712411}{4} a + \frac{220163}{8} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{5}{9} a - \frac{13}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{356}{3} a^{3} + 258 a^{2} + \frac{3817}{3} a - \frac{4861}{3}\) , \( \frac{1382}{9} a^{3} - \frac{973}{3} a^{2} - \frac{14686}{9} a + \frac{18565}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{5}{9}a-\frac{13}{9}\right){x}^{2}+\left(-\frac{356}{3}a^{3}+258a^{2}+\frac{3817}{3}a-\frac{4861}{3}\right){x}+\frac{1382}{9}a^{3}-\frac{973}{3}a^{2}-\frac{14686}{9}a+\frac{18565}{9}$ |
| 4.2-a9 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$560.4334995$ |
1.030208638 |
\( \frac{101773}{8} a^{3} - \frac{305319}{16} a^{2} - \frac{712411}{4} a + \frac{3391743}{16} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{17}{3}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{34}{9} a^{3} + \frac{41}{3} a^{2} + \frac{332}{9} a - \frac{935}{9}\) , \( -\frac{155}{9} a^{3} + \frac{118}{3} a^{2} + \frac{1666}{9} a - \frac{2251}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{17}{3}\right){x}^{2}+\left(-\frac{34}{9}a^{3}+\frac{41}{3}a^{2}+\frac{332}{9}a-\frac{935}{9}\right){x}-\frac{155}{9}a^{3}+\frac{118}{3}a^{2}+\frac{1666}{9}a-\frac{2251}{9}$ |
| 4.2-a10 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( -\frac{55573026649}{75497472} a^{3} + \frac{55573026649}{50331648} a^{2} + \frac{389011186543}{37748736} a - \frac{913768636355}{75497472} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( \frac{1}{9} a^{3} - \frac{2}{3} a^{2} - \frac{5}{9} a + \frac{23}{9}\) , \( 0\) , \( \frac{73}{9} a^{3} - \frac{11}{3} a^{2} - \frac{32}{9} a + \frac{23}{9}\) , \( \frac{1880}{9} a^{3} + \frac{1664}{3} a^{2} - \frac{7096}{9} a - \frac{1139}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}={x}^{3}+\left(\frac{1}{9}a^{3}-\frac{2}{3}a^{2}-\frac{5}{9}a+\frac{23}{9}\right){x}^{2}+\left(\frac{73}{9}a^{3}-\frac{11}{3}a^{2}-\frac{32}{9}a+\frac{23}{9}\right){x}+\frac{1880}{9}a^{3}+\frac{1664}{3}a^{2}-\frac{7096}{9}a-\frac{1139}{9}$ |
| 4.2-a11 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( \frac{110887}{1152} a^{3} - \frac{110887}{768} a^{2} - \frac{776209}{576} a + \frac{1759229}{1152} \) |
\( \bigl[\frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{13}{9}\) , \( \frac{1}{9} a^{3} - \frac{2}{3} a^{2} - \frac{5}{9} a + \frac{23}{9}\) , \( 0\) , \( -\frac{7}{9} a^{3} - \frac{1}{3} a^{2} + \frac{8}{9} a + \frac{28}{9}\) , \( -\frac{80}{9} a^{3} - \frac{56}{3} a^{2} + \frac{256}{9} a + \frac{50}{9}\bigr] \) |
${y}^2+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{13}{9}\right){x}{y}={x}^{3}+\left(\frac{1}{9}a^{3}-\frac{2}{3}a^{2}-\frac{5}{9}a+\frac{23}{9}\right){x}^{2}+\left(-\frac{7}{9}a^{3}-\frac{1}{3}a^{2}+\frac{8}{9}a+\frac{28}{9}\right){x}-\frac{80}{9}a^{3}-\frac{56}{3}a^{2}+\frac{256}{9}a+\frac{50}{9}$ |
| 4.2-a12 |
4.2-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.1083748$ |
1.030208638 |
\( -\frac{110887}{1152} a^{3} + \frac{110887}{768} a^{2} + \frac{776209}{576} a + \frac{302735}{2304} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{23}{9}\) , \( -\frac{1}{9} a^{3} - \frac{1}{3} a^{2} + \frac{14}{9} a + \frac{13}{9}\) , \( 0\) , \( \frac{7}{9} a^{3} - \frac{8}{3} a^{2} + \frac{19}{9} a + \frac{26}{9}\) , \( \frac{80}{9} a^{3} - \frac{136}{3} a^{2} + \frac{320}{9} a + \frac{58}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{23}{9}\right){x}{y}={x}^{3}+\left(-\frac{1}{9}a^{3}-\frac{1}{3}a^{2}+\frac{14}{9}a+\frac{13}{9}\right){x}^{2}+\left(\frac{7}{9}a^{3}-\frac{8}{3}a^{2}+\frac{19}{9}a+\frac{26}{9}\right){x}+\frac{80}{9}a^{3}-\frac{136}{3}a^{2}+\frac{320}{9}a+\frac{58}{9}$ |
| 4.2-b1 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.430738525 |
\( \frac{653762688677050897}{288} a^{3} - \frac{653762688677050897}{192} a^{2} - \frac{4576338820739356279}{144} a + \frac{10804727886792322055}{288} \) |
\( \bigl[1\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( -218 a^{3} + 327 a^{2} + 3052 a - 3607\) , \( -\frac{15752}{3} a^{3} + 7876 a^{2} + \frac{220528}{3} a - \frac{260344}{3}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){x}^{2}+\left(-218a^{3}+327a^{2}+3052a-3607\right){x}-\frac{15752}{3}a^{3}+7876a^{2}+\frac{220528}{3}a-\frac{260344}{3}$ |
| 4.2-b2 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$26.03575090$ |
0.430738525 |
\( \frac{67954182989}{6144} a^{3} - \frac{67954182989}{4096} a^{2} - \frac{475679280923}{3072} a + \frac{1123170616927}{6144} \) |
\( \bigl[1\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( -\frac{122}{9} a^{3} + \frac{61}{3} a^{2} + \frac{1708}{9} a - \frac{2023}{9}\) , \( -\frac{232}{3} a^{3} + 116 a^{2} + \frac{3248}{3} a - \frac{3848}{3}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){x}^{2}+\left(-\frac{122}{9}a^{3}+\frac{61}{3}a^{2}+\frac{1708}{9}a-\frac{2023}{9}\right){x}-\frac{232}{3}a^{3}+116a^{2}+\frac{3248}{3}a-\frac{3848}{3}$ |
| 4.2-b3 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.430738525 |
\( -\frac{54503407609}{18} a^{3} + \frac{54503407609}{12} a^{2} + \frac{381523853263}{9} a + \frac{55242005306}{9} \) |
\( \bigl[1\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( -\frac{22}{9} a^{3} + \frac{11}{3} a^{2} + \frac{308}{9} a - \frac{398}{9}\) , \( -6 a^{3} + 9 a^{2} + 84 a - 102\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){x}^{2}+\left(-\frac{22}{9}a^{3}+\frac{11}{3}a^{2}+\frac{308}{9}a-\frac{398}{9}\right){x}-6a^{3}+9a^{2}+84a-102$ |
| 4.2-b4 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2108.895823$ |
0.430738525 |
\( -\frac{101773}{8} a^{3} + \frac{305319}{16} a^{2} + \frac{712411}{4} a + \frac{220163}{8} \) |
\( \bigl[1\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{28}{9}\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a + \frac{10}{9}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){x}^{2}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{28}{9}\right){x}+\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a+\frac{10}{9}$ |
| 4.2-b5 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.430738525 |
\( -\frac{110887}{1152} a^{3} + \frac{110887}{768} a^{2} + \frac{776209}{576} a + \frac{302735}{2304} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{37}{9}\) , \( \frac{8}{9} a^{3} - \frac{4}{3} a^{2} - \frac{112}{9} a + \frac{130}{9}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{37}{9}\right){x}+\frac{8}{9}a^{3}-\frac{4}{3}a^{2}-\frac{112}{9}a+\frac{130}{9}$ |
| 4.2-b6 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.430738525 |
\( \frac{110887}{1152} a^{3} - \frac{110887}{768} a^{2} - \frac{776209}{576} a + \frac{1759229}{1152} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a - \frac{8}{9}\) , \( -\frac{8}{9} a^{3} + \frac{4}{3} a^{2} + \frac{112}{9} a + \frac{14}{9}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a-\frac{8}{9}\right){x}-\frac{8}{9}a^{3}+\frac{4}{3}a^{2}+\frac{112}{9}a+\frac{14}{9}$ |
| 4.2-b7 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.430738525 |
\( -\frac{55573026649}{75497472} a^{3} + \frac{55573026649}{50331648} a^{2} + \frac{389011186543}{37748736} a - \frac{913768636355}{75497472} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2 a^{3} + 3 a^{2} + 28 a + 3\) , \( \frac{212}{9} a^{3} - \frac{106}{3} a^{2} - \frac{2968}{9} a - \frac{434}{9}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-2a^{3}+3a^{2}+28a+3\right){x}+\frac{212}{9}a^{3}-\frac{106}{3}a^{2}-\frac{2968}{9}a-\frac{434}{9}$ |
| 4.2-b8 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.430738525 |
\( \frac{55573026649}{75497472} a^{3} - \frac{55573026649}{50331648} a^{2} - \frac{389011186543}{37748736} a - \frac{215919499889}{150994944} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2 a^{3} - 3 a^{2} - 28 a + 32\) , \( -\frac{212}{9} a^{3} + \frac{106}{3} a^{2} + \frac{2968}{9} a - \frac{3508}{9}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(2a^{3}-3a^{2}-28a+32\right){x}-\frac{212}{9}a^{3}+\frac{106}{3}a^{2}+\frac{2968}{9}a-\frac{3508}{9}$ |
| 4.2-b9 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.508937725$ |
0.430738525 |
\( -\frac{653762688677050897}{288} a^{3} + \frac{653762688677050897}{192} a^{2} + \frac{4576338820739356279}{144} a + \frac{2650337801950168097}{576} \) |
\( \bigl[1\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a + \frac{19}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{1964}{9} a^{3} - \frac{982}{3} a^{2} - \frac{27496}{9} a - \frac{3995}{9}\) , \( \frac{47258}{9} a^{3} - \frac{23629}{3} a^{2} - \frac{661612}{9} a - \frac{95801}{9}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a+\frac{19}{9}\right){x}^{2}+\left(\frac{1964}{9}a^{3}-\frac{982}{3}a^{2}-\frac{27496}{9}a-\frac{3995}{9}\right){x}+\frac{47258}{9}a^{3}-\frac{23629}{3}a^{2}-\frac{661612}{9}a-\frac{95801}{9}$ |
| 4.2-b10 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$26.03575090$ |
0.430738525 |
\( -\frac{67954182989}{6144} a^{3} + \frac{67954182989}{4096} a^{2} + \frac{475679280923}{3072} a + \frac{275669927173}{12288} \) |
\( \bigl[1\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a + \frac{19}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{124}{9} a^{3} - \frac{62}{3} a^{2} - \frac{1736}{9} a - \frac{235}{9}\) , \( \frac{698}{9} a^{3} - \frac{349}{3} a^{2} - \frac{9772}{9} a - \frac{1433}{9}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a+\frac{19}{9}\right){x}^{2}+\left(\frac{124}{9}a^{3}-\frac{62}{3}a^{2}-\frac{1736}{9}a-\frac{235}{9}\right){x}+\frac{698}{9}a^{3}-\frac{349}{3}a^{2}-\frac{9772}{9}a-\frac{1433}{9}$ |
| 4.2-b11 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$527.2239557$ |
0.430738525 |
\( \frac{54503407609}{18} a^{3} - \frac{54503407609}{12} a^{2} - \frac{381523853263}{9} a + \frac{1801566841885}{36} \) |
\( \bigl[1\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a + \frac{19}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{8}{3} a^{3} - 4 a^{2} - \frac{112}{3} a - \frac{20}{3}\) , \( \frac{56}{9} a^{3} - \frac{28}{3} a^{2} - \frac{784}{9} a - \frac{116}{9}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a+\frac{19}{9}\right){x}^{2}+\left(\frac{8}{3}a^{3}-4a^{2}-\frac{112}{3}a-\frac{20}{3}\right){x}+\frac{56}{9}a^{3}-\frac{28}{3}a^{2}-\frac{784}{9}a-\frac{116}{9}$ |
| 4.2-b12 |
4.2-b |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.45223$ |
$(7/9a^3-5/3a^2-71/9a+80/9), (4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2108.895823$ |
0.430738525 |
\( \frac{101773}{8} a^{3} - \frac{305319}{16} a^{2} - \frac{712411}{4} a + \frac{3391743}{16} \) |
\( \bigl[1\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a + \frac{19}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{4}{9} a^{3} - \frac{2}{3} a^{2} - \frac{56}{9} a + \frac{20}{9}\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a+\frac{19}{9}\right){x}^{2}+\left(\frac{4}{9}a^{3}-\frac{2}{3}a^{2}-\frac{56}{9}a+\frac{20}{9}\right){x}$ |
| 4.3-a1 |
4.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.45223$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.068789810$ |
$942.8701559$ |
1.430732181 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( -\frac{1}{9} a^{3} - \frac{1}{3} a^{2} + \frac{14}{9} a + \frac{22}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{11}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{23}{3} a + \frac{7}{3}\) , \( -\frac{1}{9} a^{3} - \frac{4}{3} a^{2} + \frac{41}{9} a + \frac{4}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}-\frac{1}{3}a^{2}+\frac{14}{9}a+\frac{22}{9}\right){x}^{2}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{23}{3}a+\frac{7}{3}\right){x}-\frac{1}{9}a^{3}-\frac{4}{3}a^{2}+\frac{41}{9}a+\frac{4}{9}$ |
| 4.3-a2 |
4.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.45223$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.034394905$ |
$1885.740311$ |
1.430732181 |
\( \frac{14368}{9} a^{3} - \frac{7184}{3} a^{2} - \frac{201152}{9} a + \frac{290720}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( \frac{1}{3} a^{3} - \frac{14}{3} a - \frac{4}{3}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( -\frac{2}{3} a^{3} + \frac{37}{3} a - \frac{7}{3}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} - \frac{31}{9} a - \frac{32}{9}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{14}{3}a-\frac{4}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{37}{3}a-\frac{7}{3}\right){x}-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}-\frac{31}{9}a-\frac{32}{9}$ |
| 4.3-b1 |
4.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$14.45223$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.068789810$ |
$942.8701559$ |
1.430732181 |
\( 128 a^{3} - 192 a^{2} - 1792 a + 2496 \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{11}{3}\) , \( -\frac{16}{9} a^{3} + \frac{11}{3} a^{2} + \frac{170}{9} a - \frac{179}{9}\) , \( -\frac{14}{9} a^{3} + \frac{10}{3} a^{2} + \frac{142}{9} a - \frac{196}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}{y}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){x}^{2}+\left(-\frac{16}{9}a^{3}+\frac{11}{3}a^{2}+\frac{170}{9}a-\frac{179}{9}\right){x}-\frac{14}{9}a^{3}+\frac{10}{3}a^{2}+\frac{142}{9}a-\frac{196}{9}$ |
| 4.3-b2 |
4.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.45223$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.034394905$ |
$1885.740311$ |
1.430732181 |
\( \frac{14368}{9} a^{3} - \frac{7184}{3} a^{2} - \frac{201152}{9} a + \frac{290720}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( \frac{1}{9} a^{3} - \frac{2}{3} a^{2} - \frac{14}{9} a + \frac{32}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( -\frac{11}{9} a^{3} + \frac{10}{3} a^{2} + \frac{136}{9} a - \frac{181}{9}\) , \( \frac{7}{9} a^{3} - \frac{8}{3} a^{2} - \frac{89}{9} a + \frac{116}{9}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}-\frac{2}{3}a^{2}-\frac{14}{9}a+\frac{32}{9}\right){x}^{2}+\left(-\frac{11}{9}a^{3}+\frac{10}{3}a^{2}+\frac{136}{9}a-\frac{181}{9}\right){x}+\frac{7}{9}a^{3}-\frac{8}{3}a^{2}-\frac{89}{9}a+\frac{116}{9}$ |
| 8.3-a1 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$322.1013542$ |
1.184196155 |
\( \frac{42139646}{9} a^{3} - \frac{21069823}{3} a^{2} - \frac{589955044}{9} a + \frac{704092936}{9} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{1}{3} a^{3} - \frac{11}{3} a - \frac{1}{3}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( -\frac{1007}{9} a^{3} + \frac{763}{3} a^{2} + \frac{10696}{9} a - \frac{15088}{9}\) , \( -\frac{21434}{9} a^{3} + \frac{15109}{3} a^{2} + \frac{229804}{9} a - \frac{282616}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{11}{3}a-\frac{1}{3}\right){x}^{2}+\left(-\frac{1007}{9}a^{3}+\frac{763}{3}a^{2}+\frac{10696}{9}a-\frac{15088}{9}\right){x}-\frac{21434}{9}a^{3}+\frac{15109}{3}a^{2}+\frac{229804}{9}a-\frac{282616}{9}$ |
| 8.3-a2 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$80.52533856$ |
1.184196155 |
\( -\frac{5402624050}{9} a^{3} + \frac{2701312025}{3} a^{2} + \frac{75636736700}{9} a + \frac{10951055302}{9} \) |
\( \bigl[-\frac{4}{9} a^{3} + \frac{2}{3} a^{2} + \frac{47}{9} a - \frac{20}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{32}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( \frac{133}{3} a^{3} - 51 a^{2} - \frac{1550}{3} a + \frac{248}{3}\) , \( \frac{3916}{9} a^{3} - \frac{1499}{3} a^{2} - \frac{45752}{9} a + \frac{6854}{9}\bigr] \) |
${y}^2+\left(-\frac{4}{9}a^{3}+\frac{2}{3}a^{2}+\frac{47}{9}a-\frac{20}{9}\right){x}{y}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{32}{9}\right){x}^{2}+\left(\frac{133}{3}a^{3}-51a^{2}-\frac{1550}{3}a+\frac{248}{3}\right){x}+\frac{3916}{9}a^{3}-\frac{1499}{3}a^{2}-\frac{45752}{9}a+\frac{6854}{9}$ |
| 8.3-a3 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1288.405417$ |
1.184196155 |
\( \frac{1330}{3} a^{3} - 665 a^{2} - \frac{18620}{3} a + \frac{27698}{3} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{1}{9} a^{3} - \frac{2}{3} a^{2} - \frac{5}{9} a + \frac{41}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( \frac{31}{9} a^{3} - \frac{38}{3} a^{2} - \frac{146}{9} a + \frac{308}{9}\) , \( \frac{73}{9} a^{3} - \frac{95}{3} a^{2} - \frac{158}{9} a + \frac{428}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){y}={x}^{3}+\left(\frac{1}{9}a^{3}-\frac{2}{3}a^{2}-\frac{5}{9}a+\frac{41}{9}\right){x}^{2}+\left(\frac{31}{9}a^{3}-\frac{38}{3}a^{2}-\frac{146}{9}a+\frac{308}{9}\right){x}+\frac{73}{9}a^{3}-\frac{95}{3}a^{2}-\frac{158}{9}a+\frac{428}{9}$ |
| 8.3-a4 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$322.1013542$ |
1.184196155 |
\( -\frac{686}{9} a^{3} + \frac{343}{3} a^{2} + \frac{9604}{9} a + \frac{2744}{9} \) |
\( \bigl[-\frac{4}{9} a^{3} + \frac{2}{3} a^{2} + \frac{47}{9} a - \frac{20}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{19}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( -2 a^{3} + a^{2} + 25 a + 13\) , \( -\frac{79}{9} a^{3} + \frac{35}{3} a^{2} + \frac{908}{9} a - \frac{314}{9}\bigr] \) |
${y}^2+\left(-\frac{4}{9}a^{3}+\frac{2}{3}a^{2}+\frac{47}{9}a-\frac{20}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{19}{9}\right){x}^{2}+\left(-2a^{3}+a^{2}+25a+13\right){x}-\frac{79}{9}a^{3}+\frac{35}{3}a^{2}+\frac{908}{9}a-\frac{314}{9}$ |
| 8.3-a5 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{4} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1288.405417$ |
1.184196155 |
\( -\frac{16150}{3} a^{3} + 8075 a^{2} + \frac{226100}{3} a + \frac{51934}{3} \) |
\( \bigl[-\frac{4}{9} a^{3} + \frac{2}{3} a^{2} + \frac{47}{9} a - \frac{20}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{32}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( -\frac{41}{9} a^{3} + \frac{37}{3} a^{2} + \frac{430}{9} a - \frac{781}{9}\) , \( 29 a^{3} - 53 a^{2} - 318 a + 286\bigr] \) |
${y}^2+\left(-\frac{4}{9}a^{3}+\frac{2}{3}a^{2}+\frac{47}{9}a-\frac{20}{9}\right){x}{y}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{32}{9}\right){x}^{2}+\left(-\frac{41}{9}a^{3}+\frac{37}{3}a^{2}+\frac{430}{9}a-\frac{781}{9}\right){x}+29a^{3}-53a^{2}-318a+286$ |
| 8.3-a6 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$644.2027085$ |
1.184196155 |
\( \frac{15319210}{9} a^{3} - \frac{7659605}{3} a^{2} - \frac{214468940}{9} a + \frac{253180334}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{28}{9} a + \frac{19}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{2}{3} a^{3} + a^{2} + \frac{28}{3} a - \frac{43}{3}\) , \( \frac{2}{3} a^{3} - a^{2} - \frac{28}{3} a + \frac{28}{3}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{28}{9}a+\frac{19}{9}\right){x}^{2}+\left(-\frac{2}{3}a^{3}+a^{2}+\frac{28}{3}a-\frac{43}{3}\right){x}+\frac{2}{3}a^{3}-a^{2}-\frac{28}{3}a+\frac{28}{3}$ |
| 8.3-b1 |
8.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$578.0861742$ |
2.125316817 |
\( \frac{42139646}{9} a^{3} - \frac{21069823}{3} a^{2} - \frac{589955044}{9} a + \frac{704092936}{9} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{19}{9} a + \frac{1}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( -\frac{22}{3} a^{3} + 11 a^{2} + \frac{323}{3} a - \frac{377}{3}\) , \( \frac{47}{3} a^{3} - 5 a^{2} - \frac{934}{3} a + \frac{1018}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{19}{9}a+\frac{1}{9}\right){x}^{2}+\left(-\frac{22}{3}a^{3}+11a^{2}+\frac{323}{3}a-\frac{377}{3}\right){x}+\frac{47}{3}a^{3}-5a^{2}-\frac{934}{3}a+\frac{1018}{3}$ |
| 8.3-b2 |
8.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2312.344697$ |
2.125316817 |
\( \frac{1330}{3} a^{3} - 665 a^{2} - \frac{18620}{3} a + \frac{27698}{3} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{2}{9} a^{3} - \frac{1}{3} a^{2} - \frac{19}{9} a + \frac{1}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( \frac{4}{9} a^{3} - \frac{2}{3} a^{2} - \frac{11}{9} a + \frac{29}{9}\) , \( a^{2} - 2 a\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(\frac{2}{9}a^{3}-\frac{1}{3}a^{2}-\frac{19}{9}a+\frac{1}{9}\right){x}^{2}+\left(\frac{4}{9}a^{3}-\frac{2}{3}a^{2}-\frac{11}{9}a+\frac{29}{9}\right){x}+a^{2}-2a$ |
| 8.3-b3 |
8.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$578.0861742$ |
2.125316817 |
\( -\frac{5402624050}{9} a^{3} + \frac{2701312025}{3} a^{2} + \frac{75636736700}{9} a + \frac{10951055302}{9} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{4}{9} a^{3} - \frac{2}{3} a^{2} - \frac{47}{9} a + \frac{20}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( \frac{11}{3} a^{3} - 7 a^{2} - \frac{139}{3} a + \frac{58}{3}\) , \( -\frac{71}{9} a^{3} + \frac{16}{3} a^{2} + \frac{922}{9} a + \frac{437}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){y}={x}^{3}+\left(\frac{4}{9}a^{3}-\frac{2}{3}a^{2}-\frac{47}{9}a+\frac{20}{9}\right){x}^{2}+\left(\frac{11}{3}a^{3}-7a^{2}-\frac{139}{3}a+\frac{58}{3}\right){x}-\frac{71}{9}a^{3}+\frac{16}{3}a^{2}+\frac{922}{9}a+\frac{437}{9}$ |
| 8.3-b4 |
8.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{4} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2312.344697$ |
2.125316817 |
\( -\frac{16150}{3} a^{3} + 8075 a^{2} + \frac{226100}{3} a + \frac{51934}{3} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{4}{9} a^{3} - \frac{2}{3} a^{2} - \frac{47}{9} a + \frac{20}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{14}{9} a - \frac{22}{9}\) , \( \frac{13}{9} a^{3} - \frac{11}{3} a^{2} - \frac{137}{9} a + \frac{209}{9}\) , \( \frac{19}{9} a^{3} - \frac{14}{3} a^{2} - \frac{203}{9} a + \frac{257}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{14}{9}a-\frac{22}{9}\right){y}={x}^{3}+\left(\frac{4}{9}a^{3}-\frac{2}{3}a^{2}-\frac{47}{9}a+\frac{20}{9}\right){x}^{2}+\left(\frac{13}{9}a^{3}-\frac{11}{3}a^{2}-\frac{137}{9}a+\frac{209}{9}\right){x}+\frac{19}{9}a^{3}-\frac{14}{3}a^{2}-\frac{203}{9}a+\frac{257}{9}$ |
| 8.3-b5 |
8.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$578.0861742$ |
2.125316817 |
\( -\frac{686}{9} a^{3} + \frac{343}{3} a^{2} + \frac{9604}{9} a + \frac{2744}{9} \) |
\( \bigl[-\frac{1}{3} a^{3} + a^{2} + \frac{11}{3} a - \frac{14}{3}\) , \( \frac{4}{9} a^{3} - \frac{2}{3} a^{2} - \frac{47}{9} a + \frac{29}{9}\) , \( -\frac{4}{9} a^{3} + \frac{2}{3} a^{2} + \frac{47}{9} a - \frac{20}{9}\) , \( \frac{16}{9} a^{3} - \frac{11}{3} a^{2} - \frac{161}{9} a + \frac{251}{9}\) , \( \frac{32}{9} a^{3} - \frac{19}{3} a^{2} - \frac{340}{9} a + \frac{340}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{11}{3}a-\frac{14}{3}\right){x}{y}+\left(-\frac{4}{9}a^{3}+\frac{2}{3}a^{2}+\frac{47}{9}a-\frac{20}{9}\right){y}={x}^{3}+\left(\frac{4}{9}a^{3}-\frac{2}{3}a^{2}-\frac{47}{9}a+\frac{29}{9}\right){x}^{2}+\left(\frac{16}{9}a^{3}-\frac{11}{3}a^{2}-\frac{161}{9}a+\frac{251}{9}\right){x}+\frac{32}{9}a^{3}-\frac{19}{3}a^{2}-\frac{340}{9}a+\frac{340}{9}$ |
| 8.3-b6 |
8.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(7/9a^3-5/3a^2-71/9a+80/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$289.0430871$ |
2.125316817 |
\( \frac{15319210}{9} a^{3} - \frac{7659605}{3} a^{2} - \frac{214468940}{9} a + \frac{253180334}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{10}{9}\) , \( -\frac{5}{9} a^{3} + \frac{1}{3} a^{2} + \frac{61}{9} a + \frac{11}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{32}{9}\) , \( -\frac{1}{3} a^{3} - 11 a^{2} + \frac{128}{3} a + \frac{7}{3}\) , \( \frac{140}{9} a^{3} - \frac{178}{3} a^{2} + \frac{677}{9} a + \frac{70}{9}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{10}{9}\right){x}{y}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{32}{9}\right){y}={x}^{3}+\left(-\frac{5}{9}a^{3}+\frac{1}{3}a^{2}+\frac{61}{9}a+\frac{11}{9}\right){x}^{2}+\left(-\frac{1}{3}a^{3}-11a^{2}+\frac{128}{3}a+\frac{7}{3}\right){x}+\frac{140}{9}a^{3}-\frac{178}{3}a^{2}+\frac{677}{9}a+\frac{70}{9}$ |
| 8.4-a1 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{4} \) |
$15.76027$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1288.405417$ |
1.184196155 |
\( \frac{16150}{3} a^{3} - 8075 a^{2} - \frac{226100}{3} a + \frac{286109}{3} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( -\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{5}{9} a - \frac{32}{9}\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( -\frac{653}{9} a^{3} + \frac{478}{3} a^{2} + \frac{7018}{9} a - \frac{8962}{9}\) , \( -\frac{2665}{3} a^{3} + 1914 a^{2} + \frac{28505}{3} a - \frac{36239}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{5}{9}a-\frac{32}{9}\right){x}^{2}+\left(-\frac{653}{9}a^{3}+\frac{478}{3}a^{2}+\frac{7018}{9}a-\frac{8962}{9}\right){x}-\frac{2665}{3}a^{3}+1914a^{2}+\frac{28505}{3}a-\frac{36239}{3}$ |
| 8.4-a2 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1288.405417$ |
1.184196155 |
\( -\frac{1330}{3} a^{3} + 665 a^{2} + \frac{18620}{3} a + \frac{8413}{3} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{23}{9} a - \frac{13}{9}\) , \( 0\) , \( -a^{3} - a^{2} + 5 a + 1\) , \( -\frac{98}{9} a^{3} - \frac{68}{3} a^{2} + \frac{310}{9} a + \frac{50}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){x}{y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{23}{9}a-\frac{13}{9}\right){x}^{2}+\left(-a^{3}-a^{2}+5a+1\right){x}-\frac{98}{9}a^{3}-\frac{68}{3}a^{2}+\frac{310}{9}a+\frac{50}{9}$ |
| 8.4-a3 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$15.76027$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$322.1013542$ |
1.184196155 |
\( -\frac{42139646}{9} a^{3} + \frac{21069823}{3} a^{2} + \frac{589955044}{9} a + \frac{93068069}{9} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( \frac{1}{9} a^{3} + \frac{1}{3} a^{2} - \frac{23}{9} a - \frac{13}{9}\) , \( 0\) , \( -\frac{179}{9} a^{3} - \frac{158}{3} a^{2} + \frac{625}{9} a + \frac{104}{9}\) , \( -\frac{4378}{9} a^{3} - \frac{2785}{3} a^{2} + \frac{13448}{9} a + \frac{2149}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){x}{y}={x}^{3}+\left(\frac{1}{9}a^{3}+\frac{1}{3}a^{2}-\frac{23}{9}a-\frac{13}{9}\right){x}^{2}+\left(-\frac{179}{9}a^{3}-\frac{158}{3}a^{2}+\frac{625}{9}a+\frac{104}{9}\right){x}-\frac{4378}{9}a^{3}-\frac{2785}{3}a^{2}+\frac{13448}{9}a+\frac{2149}{9}$ |
| 8.4-a4 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$15.76027$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$322.1013542$ |
1.184196155 |
\( \frac{686}{9} a^{3} - \frac{343}{3} a^{2} - \frac{9604}{9} a + \frac{12691}{9} \) |
\( \bigl[-\frac{1}{9} a^{3} + \frac{2}{3} a^{2} + \frac{14}{9} a - \frac{23}{9}\) , \( \frac{5}{9} a^{3} - \frac{1}{3} a^{2} - \frac{61}{9} a - \frac{11}{9}\) , \( 0\) , \( -16 a^{3} + 79 a^{2} - 42 a - 7\) , \( -\frac{668}{9} a^{3} + \frac{1156}{3} a^{2} - \frac{2852}{9} a - \frac{496}{9}\bigr] \) |
${y}^2+\left(-\frac{1}{9}a^{3}+\frac{2}{3}a^{2}+\frac{14}{9}a-\frac{23}{9}\right){x}{y}={x}^{3}+\left(\frac{5}{9}a^{3}-\frac{1}{3}a^{2}-\frac{61}{9}a-\frac{11}{9}\right){x}^{2}+\left(-16a^{3}+79a^{2}-42a-7\right){x}-\frac{668}{9}a^{3}+\frac{1156}{3}a^{2}-\frac{2852}{9}a-\frac{496}{9}$ |
| 8.4-a5 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$80.52533856$ |
1.184196155 |
\( \frac{5402624050}{9} a^{3} - \frac{2701312025}{3} a^{2} - \frac{75636736700}{9} a + \frac{89289104027}{9} \) |
\( \bigl[-\frac{4}{9} a^{3} + \frac{2}{3} a^{2} + \frac{47}{9} a - \frac{11}{9}\) , \( a + 1\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{19}{9} a - \frac{10}{9}\) , \( 7 a^{3} - 26 a^{2} + 36 a + 2\) , \( \frac{670}{9} a^{3} - \frac{638}{3} a^{2} + \frac{1312}{9} a + \frac{191}{9}\bigr] \) |
${y}^2+\left(-\frac{4}{9}a^{3}+\frac{2}{3}a^{2}+\frac{47}{9}a-\frac{11}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{19}{9}a-\frac{10}{9}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a^{3}-26a^{2}+36a+2\right){x}+\frac{670}{9}a^{3}-\frac{638}{3}a^{2}+\frac{1312}{9}a+\frac{191}{9}$ |
| 8.4-a6 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$15.76027$ |
$(4/9a^3-2/3a^2-47/9a+29/9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$644.2027085$ |
1.184196155 |
\( -\frac{15319210}{9} a^{3} + \frac{7659605}{3} a^{2} + \frac{214468940}{9} a + \frac{31051789}{9} \) |
\( \bigl[-\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( 0\) , \( -\frac{2}{9} a^{3} + \frac{1}{3} a^{2} + \frac{28}{9} a - \frac{1}{9}\) , \( \frac{10}{9} a^{3} - \frac{5}{3} a^{2} - \frac{140}{9} a - \frac{22}{9}\) , \( -\frac{4}{9} a^{3} + \frac{2}{3} a^{2} + \frac{56}{9} a + \frac{7}{9}\bigr] \) |
${y}^2+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){x}{y}+\left(-\frac{2}{9}a^{3}+\frac{1}{3}a^{2}+\frac{28}{9}a-\frac{1}{9}\right){y}={x}^{3}+\left(\frac{10}{9}a^{3}-\frac{5}{3}a^{2}-\frac{140}{9}a-\frac{22}{9}\right){x}-\frac{4}{9}a^{3}+\frac{2}{3}a^{2}+\frac{56}{9}a+\frac{7}{9}$ |
*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.
