| 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 |
\( -1666 a^{2} + 14713 \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a + 4\) , \( -a^{2} + 2 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a+4\right){x}-a^{2}+2a+1$ |
*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.
