| 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 |
| 1.1-a1 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$45.31995947$ |
0.697230145 |
\( -\frac{442684431359082485}{4} a^{3} - 75781116877013025 a^{2} + \frac{3776597934503821295}{4} a + \frac{1292996948609533475}{2} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{11}{4} a^{3} + \frac{3}{2} a^{2} + \frac{95}{4} a - \frac{25}{2}\) , \( -\frac{19}{4} a^{3} + 5 a^{2} + \frac{129}{4} a - \frac{43}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{11}{4}a^{3}+\frac{3}{2}a^{2}+\frac{95}{4}a-\frac{25}{2}\right){x}-\frac{19}{4}a^{3}+5a^{2}+\frac{129}{4}a-\frac{43}{2}$ |
| 1.1-a2 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( -\frac{400474515}{4} a^{3} - 68547300 a^{2} + \frac{3416462805}{4} a + \frac{1169693575}{2} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{15}{4} a + \frac{5}{2}\) , \( -\frac{3}{4} a^{3} + a^{2} + \frac{9}{4} a + \frac{3}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{1}{4}a^{3}-a^{2}+\frac{15}{4}a+\frac{5}{2}\right){x}-\frac{3}{4}a^{3}+a^{2}+\frac{9}{4}a+\frac{3}{2}$ |
| 1.1-a3 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( -\frac{93903915}{4} a^{3} + 68547300 a^{2} + \frac{44186205}{4} a - \frac{64157825}{2} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( a^{3} + \frac{3}{2} a^{2} - \frac{21}{2} a - 8\) , \( -\frac{9}{4} a^{3} - a^{2} + \frac{75}{4} a + \frac{21}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(a^{3}+\frac{3}{2}a^{2}-\frac{21}{2}a-8\right){x}-\frac{9}{4}a^{3}-a^{2}+\frac{75}{4}a+\frac{21}{2}$ |
| 1.1-a4 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$45.31995947$ |
0.697230145 |
\( -\frac{103780973863960535}{4} a^{3} + 75781116877013025 a^{2} + \frac{48659902057479845}{4} a - \frac{71063155176700975}{2} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} - \frac{17}{4} a - \frac{1}{2}\) , \( -\frac{21}{4} a^{3} - 5 a^{2} + \frac{151}{4} a + \frac{47}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{1}{4}a^{3}-a^{2}-\frac{17}{4}a-\frac{1}{2}\right){x}-\frac{21}{4}a^{3}-5a^{2}+\frac{151}{4}a+\frac{47}{2}$ |
| 1.1-a5 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( \frac{93903915}{4} a^{3} + 68547300 a^{2} - \frac{44186205}{4} a - \frac{64157825}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{3}{4} a^{3} + a^{2} + \frac{29}{4} a - \frac{13}{2}\) , \( \frac{9}{4} a^{3} - a^{2} - \frac{75}{4} a + \frac{21}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a+\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{3}{4}a^{3}+a^{2}+\frac{29}{4}a-\frac{13}{2}\right){x}+\frac{9}{4}a^{3}-a^{2}-\frac{75}{4}a+\frac{21}{2}$ |
| 1.1-a6 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$45.31995947$ |
0.697230145 |
\( \frac{103780973863960535}{4} a^{3} + 75781116877013025 a^{2} - \frac{48659902057479845}{4} a - \frac{71063155176700975}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} + a + 1\) , \( \frac{21}{4} a^{3} - 5 a^{2} - \frac{151}{4} a + \frac{47}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a+\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+a+1\right){x}+\frac{21}{4}a^{3}-5a^{2}-\frac{151}{4}a+\frac{47}{2}$ |
| 1.1-a7 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$45.31995947$ |
0.697230145 |
\( \frac{442684431359082485}{4} a^{3} - 75781116877013025 a^{2} - \frac{3776597934503821295}{4} a + \frac{1292996948609533475}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{5}{2}\) , \( 0\) , \( 2 a^{3} + 2 a^{2} - 16 a - 12\) , \( \frac{41}{4} a^{3} + 9 a^{2} - \frac{315}{4} a - \frac{111}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{13}{4}a+\frac{5}{2}\right){x}^{2}+\left(2a^{3}+2a^{2}-16a-12\right){x}+\frac{41}{4}a^{3}+9a^{2}-\frac{315}{4}a-\frac{111}{2}$ |
| 1.1-a8 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( \frac{400474515}{4} a^{3} - 68547300 a^{2} - \frac{3416462805}{4} a + \frac{1169693575}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{5}{2}\) , \( 0\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{13}{4}a+\frac{5}{2}\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+3\right){x}$ |
| 1.1-a9 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( \frac{644766235}{4} a^{3} + 470821125 a^{2} - \frac{302212945}{4} a - \frac{441539875}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a + \frac{1}{2}\) , \( a\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a - 2\) , \( -a^{3} + \frac{1}{2} a^{2} + \frac{17}{2} a - 6\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{11}{4}a+\frac{1}{2}\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a-2\right){x}-a^{3}+\frac{1}{2}a^{2}+\frac{17}{2}a-6$ |
| 1.1-a10 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( -\frac{2750341585}{4} a^{3} - 470821125 a^{2} + \frac{23463541795}{4} a + \frac{8033240375}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a + \frac{1}{2}\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{3}{4} a + \frac{1}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{11}{4}a+\frac{1}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){x}+\frac{1}{4}a^{3}-a^{2}-\frac{3}{4}a+\frac{1}{2}$ |
| 1.1-a11 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( -\frac{644766235}{4} a^{3} + 470821125 a^{2} + \frac{302212945}{4} a - \frac{441539875}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( 0\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 2\) , \( a^{3} + \frac{1}{2} a^{2} - \frac{17}{2} a - 6\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-2\right){x}+a^{3}+\frac{1}{2}a^{2}-\frac{17}{2}a-6$ |
| 1.1-a12 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$725.1193516$ |
0.697230145 |
\( \frac{2750341585}{4} a^{3} - 470821125 a^{2} - \frac{23463541795}{4} a + \frac{8033240375}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( 0\) , \( a + 1\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{1}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} - \frac{1}{4} a + \frac{1}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{1}{4}a-\frac{1}{2}\right){x}-\frac{1}{4}a^{3}-a^{2}-\frac{1}{4}a+\frac{1}{2}$ |
| 1.1-b1 |
1.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$16$ |
\( 1 \) |
$1$ |
$6.064464955$ |
0.373197843 |
\( 35735839572482 a^{2} - 16755503336993 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{13}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{101}{2} a^{3} - 150 a^{2} + \frac{21}{2} a + 59\) , \( -\frac{1937}{2} a^{3} - 2836 a^{2} + \frac{855}{2} a + 1309\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{13}{4}a-\frac{5}{2}\right){x}^{2}+\left(-\frac{101}{2}a^{3}-150a^{2}+\frac{21}{2}a+59\right){x}-\frac{1937}{2}a^{3}-2836a^{2}+\frac{855}{2}a+1309$ |
| 1.1-b2 |
1.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 1 \) |
$1$ |
$97.03143928$ |
0.373197843 |
\( 16974593 \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 5 a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{29}{2} a^{3} + 7 a^{2} + \frac{255}{2} a - 74\) , \( -\frac{123}{2} a^{3} + 39 a^{2} + \frac{1059}{2} a - 353\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+5a+2\right){x}^{2}+\left(-\frac{29}{2}a^{3}+7a^{2}+\frac{255}{2}a-74\right){x}-\frac{123}{2}a^{3}+39a^{2}+\frac{1059}{2}a-353$ |
| 1.1-b3 |
1.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1552.503028$ |
0.373197843 |
\( 4913 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{7}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a + \frac{3}{2}\) , \( \frac{9}{4} a^{3} + \frac{3}{2} a^{2} - \frac{73}{4} a - \frac{25}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{13}{4}a+\frac{7}{2}\right){x}^{2}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a+\frac{3}{2}\right){x}+\frac{9}{4}a^{3}+\frac{3}{2}a^{2}-\frac{73}{4}a-\frac{25}{2}$ |
| 1.1-b4 |
1.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$16$ |
\( 1 \) |
$1$ |
$6.064464955$ |
0.373197843 |
\( -35735839572482 a^{2} + 304867052815345 \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( a - 1\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{109}{4} a^{3} + \frac{29}{2} a^{2} + \frac{1037}{4} a - \frac{389}{2}\) , \( -205 a^{3} + 109 a^{2} + 1882 a - 1312\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{109}{4}a^{3}+\frac{29}{2}a^{2}+\frac{1037}{4}a-\frac{389}{2}\right){x}-205a^{3}+109a^{2}+1882a-1312$ |
| 1.1-b5 |
1.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1552.503028$ |
0.373197843 |
\( 1666 a^{2} - 281 \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 6\) , \( a^{2} - 2 a - 7\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+6\right){x}+a^{2}-2a-7$ |
| 1.1-b6 |
1.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.80834$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$1552.503028$ |
0.373197843 |
\( -1666 a^{2} + 14713 \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a + 4\) , \( -a^{2} + 2 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a+4\right){x}-a^{2}+2a+1$ |
| 9.1-a1 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( -\frac{154923293928233}{36} a^{3} + \frac{113127908180881}{9} a^{2} + \frac{8070385953855}{4} a - \frac{106082906998489}{18} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{883}{2} a^{3} + 299 a^{2} + \frac{7557}{2} a - 2587\) , \( -\frac{46471}{4} a^{3} + 7963 a^{2} + \frac{396341}{4} a - \frac{135709}{2}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{883}{2}a^{3}+299a^{2}+\frac{7557}{2}a-2587\right){x}-\frac{46471}{4}a^{3}+7963a^{2}+\frac{396341}{4}a-\frac{135709}{2}$ |
| 9.1-a2 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( \frac{573152115635}{4} a^{3} + \frac{3766653496885}{9} a^{2} - \frac{2418610218709}{36} a - \frac{3532150159265}{18} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( -\frac{3}{4} a^{3} + \frac{3}{2} a^{2} + \frac{7}{4} a + \frac{3}{2}\) , \( 6 a^{3} - 17 a^{2} - 5 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}^{2}+\left(-\frac{3}{4}a^{3}+\frac{3}{2}a^{2}+\frac{7}{4}a+\frac{3}{2}\right){x}+6a^{3}-17a^{2}-5a+7$ |
| 9.1-a3 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{32} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$45.64451500$ |
1.404446615 |
\( -\frac{7438939205}{172186884} a^{3} + \frac{81828331255}{172186884} a + \frac{74445322141}{86093442} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -a - 1\) , \( 0\) , \( -a^{3} + 7 a + 6\) , \( \frac{3}{4} a^{3} + 2 a^{2} - \frac{41}{4} a - \frac{13}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{3}+7a+6\right){x}+\frac{3}{4}a^{3}+2a^{2}-\frac{41}{4}a-\frac{13}{2}$ |
| 9.1-a4 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$730.3122400$ |
1.404446615 |
\( \frac{3793055}{26244} a^{3} - \frac{41723605}{26244} a + \frac{46302551}{13122} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -a - 1\) , \( 0\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{3}{2}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{3}{2}\right){x}$ |
| 9.1-a5 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$730.3122400$ |
1.404446615 |
\( -\frac{173440291}{324} a^{3} + \frac{58614046}{81} a^{2} + \frac{692463097}{324} a + \frac{17417387}{18} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{111}{4} a^{3} + 19 a^{2} + \frac{949}{4} a - \frac{329}{2}\) , \( -\frac{319}{2} a^{3} + 109 a^{2} + \frac{2723}{2} a - 933\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{111}{4}a^{3}+19a^{2}+\frac{949}{4}a-\frac{329}{2}\right){x}-\frac{319}{2}a^{3}+109a^{2}+\frac{2723}{2}a-933$ |
| 9.1-a6 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$730.3122400$ |
1.404446615 |
\( \frac{434249761}{324} a^{3} - \frac{58614046}{81} a^{2} - \frac{3561367267}{324} a + \frac{134645479}{18} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{55}{4} a^{3} - 40 a^{2} + \frac{33}{4} a + \frac{45}{2}\) , \( -\frac{513}{4} a^{3} - \frac{751}{2} a^{2} + \frac{233}{4} a + \frac{351}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{9}{4}a+\frac{3}{2}\right){x}^{2}+\left(-\frac{55}{4}a^{3}-40a^{2}+\frac{33}{4}a+\frac{45}{2}\right){x}-\frac{513}{4}a^{3}-\frac{751}{2}a^{2}+\frac{233}{4}a+\frac{351}{2}$ |
| 9.1-a7 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( -\frac{22003355573863}{36} a^{3} - \frac{3766653496885}{9} a^{2} + \frac{20857051342593}{4} a + \frac{64267612784665}{18} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{5}{4} a - \frac{1}{2}\) , \( a\) , \( 2 a^{3} - a^{2} - 19 a + 13\) , \( -\frac{45}{2} a^{3} + \frac{31}{2} a^{2} + 191 a - 131\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{7}{4}a+\frac{1}{2}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{5}{4}a-\frac{1}{2}\right){x}^{2}+\left(2a^{3}-a^{2}-19a+13\right){x}-\frac{45}{2}a^{3}+\frac{31}{2}a^{2}+191a-131$ |
| 9.1-a8 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( \frac{73426453987189}{4} a^{3} - \frac{113127908180881}{9} a^{2} - \frac{5637696185105843}{36} a + \frac{1930219440257369}{18} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{35}{4} a^{3} - 35 a^{2} - \frac{47}{4} a + \frac{15}{2}\) , \( -\frac{679}{4} a^{3} - 499 a^{2} + \frac{401}{4} a + \frac{497}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{9}{4}a+\frac{3}{2}\right){x}^{2}+\left(-\frac{35}{4}a^{3}-35a^{2}-\frac{47}{4}a+\frac{15}{2}\right){x}-\frac{679}{4}a^{3}-499a^{2}+\frac{401}{4}a+\frac{497}{2}$ |
| 9.2-a1 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( \frac{154923293928233}{36} a^{3} + \frac{113127908180881}{9} a^{2} - \frac{8070385953855}{4} a - \frac{106082906998489}{18} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -45 a^{3} + \frac{69}{2} a^{2} + \frac{775}{2} a - 305\) , \( -\frac{2855}{4} a^{3} + \frac{997}{2} a^{2} + \frac{24339}{4} a - \frac{8481}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}^{2}+\left(-45a^{3}+\frac{69}{2}a^{2}+\frac{775}{2}a-305\right){x}-\frac{2855}{4}a^{3}+\frac{997}{2}a^{2}+\frac{24339}{4}a-\frac{8481}{2}$ |
| 9.2-a2 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( -\frac{573152115635}{4} a^{3} + \frac{3766653496885}{9} a^{2} + \frac{2418610218709}{36} a - \frac{3532150159265}{18} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{4} a + \frac{5}{2}\) , \( a\) , \( a^{3} + \frac{3}{2} a^{2} - \frac{11}{2} a + 1\) , \( -\frac{19}{4} a^{3} - 15 a^{2} + \frac{5}{4} a + \frac{17}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{7}{4}a+\frac{1}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{5}{4}a+\frac{5}{2}\right){x}^{2}+\left(a^{3}+\frac{3}{2}a^{2}-\frac{11}{2}a+1\right){x}-\frac{19}{4}a^{3}-15a^{2}+\frac{5}{4}a+\frac{17}{2}$ |
| 9.2-a3 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$45.64451500$ |
1.404446615 |
\( \frac{7438939205}{172186884} a^{3} - \frac{81828331255}{172186884} a + \frac{74445322141}{86093442} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( a - 1\) , \( 0\) , \( a^{3} - 7 a + 6\) , \( -\frac{3}{4} a^{3} + 2 a^{2} + \frac{41}{4} a - \frac{13}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{3}-7a+6\right){x}-\frac{3}{4}a^{3}+2a^{2}+\frac{41}{4}a-\frac{13}{2}$ |
| 9.2-a4 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$730.3122400$ |
1.404446615 |
\( -\frac{3793055}{26244} a^{3} + \frac{41723605}{26244} a + \frac{46302551}{13122} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{9}{4} a + \frac{7}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{11}{4} a + \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{9}{4}a+\frac{7}{2}\right){x}^{2}+\left(-\frac{1}{4}a^{3}-a^{2}+\frac{11}{4}a+\frac{5}{2}\right){x}-\frac{1}{2}a^{2}+\frac{1}{2}a$ |
| 9.2-a5 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$730.3122400$ |
1.404446615 |
\( \frac{173440291}{324} a^{3} + \frac{58614046}{81} a^{2} - \frac{692463097}{324} a + \frac{17417387}{18} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{115}{2} a^{3} + \frac{79}{2} a^{2} + 490 a - 335\) , \( -548 a^{3} + 375 a^{2} + 4676 a - 3202\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}^{2}+\left(-\frac{115}{2}a^{3}+\frac{79}{2}a^{2}+490a-335\right){x}-548a^{3}+375a^{2}+4676a-3202$ |
| 9.2-a6 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$730.3122400$ |
1.404446615 |
\( -\frac{434249761}{324} a^{3} - \frac{58614046}{81} a^{2} + \frac{3561367267}{324} a + \frac{134645479}{18} \) |
\( \bigl[1\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{9}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{13}{2} a^{3} - \frac{39}{2} a^{2} + 3 a + 9\) , \( -\frac{149}{4} a^{3} - \frac{219}{2} a^{2} + \frac{65}{4} a + \frac{101}{2}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{9}{4}a+\frac{3}{2}\right){x}^{2}+\left(-\frac{13}{2}a^{3}-\frac{39}{2}a^{2}+3a+9\right){x}-\frac{149}{4}a^{3}-\frac{219}{2}a^{2}+\frac{65}{4}a+\frac{101}{2}$ |
| 9.2-a7 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( \frac{22003355573863}{36} a^{3} - \frac{3766653496885}{9} a^{2} - \frac{20857051342593}{4} a + \frac{64267612784665}{18} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a - 2\) , \( a + 1\) , \( -2 a^{3} - 2 a^{2} + 16 a + 17\) , \( \frac{83}{4} a^{3} + \frac{29}{2} a^{2} - \frac{711}{4} a - \frac{249}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+4a-2\right){x}^{2}+\left(-2a^{3}-2a^{2}+16a+17\right){x}+\frac{83}{4}a^{3}+\frac{29}{2}a^{2}-\frac{711}{4}a-\frac{249}{2}$ |
| 9.2-a8 |
9.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$7.64420$ |
$(1/4a^3-11/4a+1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.5780600$ |
1.404446615 |
\( -\frac{73426453987189}{4} a^{3} - \frac{113127908180881}{9} a^{2} + \frac{5637696185105843}{36} a + \frac{1930219440257369}{18} \) |
\( \bigl[1\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{9}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{391}{4} a^{3} - \frac{599}{2} a^{2} - \frac{13}{4} a + \frac{213}{2}\) , \( -\frac{5475}{2} a^{3} - \frac{15927}{2} a^{2} + 1402 a + 3815\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{1}{2}a^{2}+\frac{9}{4}a+\frac{3}{2}\right){x}^{2}+\left(-\frac{391}{4}a^{3}-\frac{599}{2}a^{2}-\frac{13}{4}a+\frac{213}{2}\right){x}-\frac{5475}{2}a^{3}-\frac{15927}{2}a^{2}+1402a+3815$ |
| 16.1-a1 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$77.55707633$ |
1.193185789 |
\( -\frac{1108421751675}{32} a^{3} + \frac{3237481873115}{32} a^{2} + \frac{259868389725}{16} a - \frac{189747774535}{4} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( a\) , \( -\frac{111}{2} a^{3} - 161 a^{2} + \frac{59}{2} a + 79\) , \( \frac{2081}{2} a^{3} + \frac{6081}{2} a^{2} - 482 a - 1422\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{111}{2}a^{3}-161a^{2}+\frac{59}{2}a+79\right){x}+\frac{2081}{2}a^{3}+\frac{6081}{2}a^{2}-482a-1422$ |
| 16.1-a2 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$77.55707633$ |
1.193185789 |
\( \frac{1108421751675}{32} a^{3} + \frac{3237481873115}{32} a^{2} - \frac{259868389725}{16} a - \frac{189747774535}{4} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( a + 1\) , \( -23 a^{3} - 66 a^{2} + 16 a + 36\) , \( -\frac{1169}{4} a^{3} - \frac{1707}{2} a^{2} + \frac{545}{4} a + \frac{799}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{5}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{1}{2}\right){x}^{2}+\left(-23a^{3}-66a^{2}+16a+36\right){x}-\frac{1169}{4}a^{3}-\frac{1707}{2}a^{2}+\frac{545}{4}a+\frac{799}{2}$ |
| 16.1-a3 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$77.55707633$ |
1.193185789 |
\( \frac{6318305}{4096} a^{2} - \frac{641965}{1024} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{5}{2}\) , \( 0\) , \( -\frac{1}{4} a^{3} - 3 a^{2} - \frac{13}{4} a + \frac{9}{2}\) , \( -a^{3} - 4 a^{2} - a + 3\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){x}{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{9}{4}a+\frac{5}{2}\right){x}^{2}+\left(-\frac{1}{4}a^{3}-3a^{2}-\frac{13}{4}a+\frac{9}{2}\right){x}-a^{3}-4a^{2}-a+3$ |
| 16.1-a4 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$77.55707633$ |
1.193185789 |
\( \frac{9456058985625}{64} a^{3} - \frac{3237481873115}{32} a^{2} - \frac{80670843863925}{64} a + \frac{27619354661755}{32} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( 0\) , \( -\frac{45}{4} a^{3} + \frac{23}{2} a^{2} + \frac{405}{4} a - \frac{185}{2}\) , \( -63 a^{3} + 37 a^{2} + 547 a - 325\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}^{2}+\left(-\frac{45}{4}a^{3}+\frac{23}{2}a^{2}+\frac{405}{4}a-\frac{185}{2}\right){x}-63a^{3}+37a^{2}+547a-325$ |
| 16.1-a5 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$77.55707633$ |
1.193185789 |
\( -\frac{9456058985625}{64} a^{3} - \frac{3237481873115}{32} a^{2} + \frac{80670843863925}{64} a + \frac{27619354661755}{32} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( 1\) , \( -\frac{65}{2} a^{3} + 24 a^{2} + \frac{567}{2} a - 204\) , \( \frac{1077}{4} a^{3} - 176 a^{2} - \frac{9263}{4} a + \frac{3149}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{1}{2}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}^{2}+\left(-\frac{65}{2}a^{3}+24a^{2}+\frac{567}{2}a-204\right){x}+\frac{1077}{4}a^{3}-176a^{2}-\frac{9263}{4}a+\frac{3149}{2}$ |
| 16.1-a6 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$77.55707633$ |
1.193185789 |
\( -\frac{6318305}{4096} a^{2} + \frac{54296885}{4096} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( 0\) , \( \frac{11}{4} a^{3} + 3 a^{2} - \frac{97}{4} a - \frac{45}{2}\) , \( 5 a^{3} + 4 a^{2} - 43 a - 33\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{7}{4}a+\frac{1}{2}\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}^{2}+\left(\frac{11}{4}a^{3}+3a^{2}-\frac{97}{4}a-\frac{45}{2}\right){x}+5a^{3}+4a^{2}-43a-33$ |
| 16.1-b1 |
16.1-b |
$6$ |
$45$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$1.304759140$ |
0.501830438 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( 1\) , \( 1\) , \( -\frac{75}{4} a^{3} + \frac{825}{4} a - \frac{269}{2}\) , \( -\frac{507}{4} a^{3} + \frac{5577}{4} a - \frac{1833}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-\frac{75}{4}a^{3}+\frac{825}{4}a-\frac{269}{2}\right){x}-\frac{507}{4}a^{3}+\frac{5577}{4}a-\frac{1833}{2}$ |
| 16.1-b2 |
16.1-b |
$6$ |
$45$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$1.304759140$ |
0.501830438 |
\( \frac{1250637664527933}{128} a^{3} - \frac{13757014309807263}{128} a - \frac{4509238226399579}{64} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{29}{4} a^{3} - \frac{319}{4} a - \frac{25}{2}\) , \( 13 a^{3} - 143 a - 132\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){y}={x}^{3}+{x}^{2}+\left(\frac{29}{4}a^{3}-\frac{319}{4}a-\frac{25}{2}\right){x}+13a^{3}-143a-132$ |
| 16.1-b3 |
16.1-b |
$6$ |
$45$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$815.4744629$ |
0.501830438 |
\( -\frac{461373}{8} a^{3} + \frac{5075103}{8} a - \frac{1664219}{4} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{5}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a + \frac{1}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){y}={x}^{3}+{x}^{2}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a-\frac{5}{2}\right){x}+\frac{1}{4}a^{3}-\frac{11}{4}a+\frac{1}{2}$ |
| 16.1-b4 |
16.1-b |
$6$ |
$45$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$1.304759140$ |
0.501830438 |
\( -\frac{1250637664527933}{128} a^{3} + \frac{13757014309807263}{128} a - \frac{4509238226399579}{64} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( -7 a^{3} + 77 a - 13\) , \( -\frac{51}{4} a^{3} + \frac{561}{4} a - \frac{265}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){y}={x}^{3}+{x}^{2}+\left(-7a^{3}+77a-13\right){x}-\frac{51}{4}a^{3}+\frac{561}{4}a-\frac{265}{2}$ |
| 16.1-b5 |
16.1-b |
$6$ |
$45$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$815.4744629$ |
0.501830438 |
\( \frac{461373}{8} a^{3} - \frac{5075103}{8} a - \frac{1664219}{4} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{2} a^{3} - \frac{11}{2} a - 3\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){y}={x}^{3}+{x}^{2}+\left(\frac{1}{2}a^{3}-\frac{11}{2}a-3\right){x}$ |
| 16.1-b6 |
16.1-b |
$6$ |
$45$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.21423$ |
$(1/2a^3-9/2a+1), (1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$815.4744629$ |
0.501830438 |
\( \frac{1331}{8} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{1}{2}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{11}{4}a+\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{11}{4}a-\frac{3}{2}\right){x}^{2}$ |
| 16.2-a1 |
16.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.21423$ |
$(1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$300.4971488$ |
1.155758264 |
\( \frac{215383}{4} a^{3} - \frac{75735}{2} a^{2} - \frac{1836835}{4} a + \frac{646019}{2} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{3}{4} a - \frac{11}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{5}{4} a - \frac{5}{2}\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}^{2}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{3}{4}a-\frac{11}{2}\right){x}-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{5}{4}a-\frac{5}{2}$ |
| 16.2-a2 |
16.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.21423$ |
$(1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$300.4971488$ |
1.155758264 |
\( -\frac{215383}{4} a^{3} - \frac{75735}{2} a^{2} + \frac{1836835}{4} a + \frac{646019}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{4} a - \frac{11}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{5}{4} a - \frac{5}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{3}{2}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}^{2}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{4}a-\frac{11}{2}\right){x}+\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{5}{4}a-\frac{5}{2}$ |
| 16.2-a3 |
16.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{16} \) |
$8.21423$ |
$(1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$300.4971488$ |
1.155758264 |
\( -\frac{115027211667}{4} a^{3} + \frac{167992107919}{2} a^{2} + \frac{53932500751}{4} a - \frac{78766512219}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( a + 1\) , \( -101 a^{3} + 66 a^{2} + 878 a - 611\) , \( \frac{5255}{4} a^{3} - 934 a^{2} - \frac{44373}{4} a + \frac{15265}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{3}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}^{2}+\left(-101a^{3}+66a^{2}+878a-611\right){x}+\frac{5255}{4}a^{3}-934a^{2}-\frac{44373}{4}a+\frac{15265}{2}$ |
| 16.2-a4 |
16.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$8.21423$ |
$(1/4a^3+1/2a^2-5/4a-1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$1201.988595$ |
1.155758264 |
\( \frac{19570419}{4} a^{3} - \frac{6521955}{2} a^{2} - \frac{166164207}{4} a + \frac{56809759}{2} \) |
\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( a + 1\) , \( -a^{3} - 5 a^{2} - 2 a + 7\) , \( -\frac{21}{4} a^{3} - 15 a^{2} + \frac{3}{4} a + \frac{17}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{9}{4}a-\frac{3}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-a^{3}-5a^{2}-2a+7\right){x}-\frac{21}{4}a^{3}-15a^{2}+\frac{3}{4}a+\frac{17}{2}$ |
*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.
