| 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 |
| 468.1-a1 |
468.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{5} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.121607637$ |
$16.07577957$ |
2.168808513 |
\( -\frac{10910603}{16848} a + \frac{24760295}{16848} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(a-1\right){x}+a-1$ |
| 468.1-a2 |
468.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{2} \cdot 3^{17} \cdot 13^{4} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.121607637$ |
$4.018944894$ |
2.168808513 |
\( \frac{7269976942057}{14549791698} a + \frac{9471148876247}{14549791698} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -9 a - 11\) , \( -45 a + 63\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-9a-11\right){x}-45a+63$ |
| 468.1-a3 |
468.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{10} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.060803818$ |
$16.07577957$ |
2.168808513 |
\( \frac{9005501747}{341172} a + \frac{7518764437}{85293} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( a - 21\) , \( -3 a + 27\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(a-21\right){x}-3a+27$ |
| 468.1-a4 |
468.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{2} \cdot 3^{8} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.121607637$ |
$16.07577957$ |
2.168808513 |
\( \frac{3728428935841}{702} a + \frac{20491399638653}{2106} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 351\) , \( -137 a + 2343\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-351\right){x}-137a+2343$ |
| 468.1-b1 |
468.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{6} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.942653879$ |
1.370845538 |
\( \frac{26993975}{202176} a - \frac{19312621}{5184} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -7 a - 12\) , \( -29 a - 35\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-7a-12\right){x}-29a-35$ |
| 468.1-b2 |
468.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{12} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.942653879$ |
1.370845538 |
\( -\frac{7218745488379}{6141096} a + \frac{5026487138908}{255879} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -127 a - 212\) , \( -1373 a - 1651\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-127a-212\right){x}-1373a-1651$ |
| 468.1-c1 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{6} \cdot 3^{5} \cdot 13^{4} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.683867782$ |
0.758683186 |
\( -\frac{443211926632839962731}{9126} a + \frac{314036192923802908687}{2808} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 1438 a - 3583\) , \( 44631 a - 99292\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1438a-3583\right){x}+44631a-99292$ |
| 468.1-c2 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{2} \cdot 3^{7} \cdot 13^{12} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.683867782$ |
0.758683186 |
\( -\frac{1092614702272471}{7037487522} a + \frac{839661935060549}{2345829174} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 278 a + 168\) , \( -4212 a - 6574\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(278a+168\right){x}-4212a-6574$ |
| 468.1-c3 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{24} \cdot 3^{5} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( \frac{542092739}{89856} a - \frac{17054358785}{1437696} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -2 a - 23\) , \( 15 a - 28\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2a-23\right){x}+15a-28$ |
| 468.1-c4 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{14} \cdot 13^{6} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( \frac{4879813408027}{4670303508} a + \frac{1228664479915}{389191959} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -112 a - 162\) , \( -678 a - 892\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-112a-162\right){x}-678a-892$ |
| 468.1-c5 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{2} \cdot 3^{28} \cdot 13^{3} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( -\frac{3728957993280250657}{95461183330578} a + \frac{3241728832543771523}{31820394443526} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -502 a - 812\) , \( 8760 a + 12134\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-502a-812\right){x}+8760a+12134$ |
| 468.1-c6 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{10} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( -\frac{8774349664979}{75816} a + \frac{162358551869077}{606528} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -2 a - 343\) , \( 1359 a - 796\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2a-343\right){x}+1359a-796$ |
| 468.1-c7 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{7} \cdot 13^{3} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( \frac{12474776946521}{1971216} a + \frac{5418370843313}{657072} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -130 a + 299\) , \( 169 a - 394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-130a+299\right){x}+169a-394$ |
| 468.1-c8 |
468.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{20} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( \frac{5329029126891668773}{13817466} a + \frac{27770118449383467827}{55269864} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1442 a - 2223\) , \( 44103 a + 54948\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1442a-2223\right){x}+44103a+54948$ |
| 468.1-d1 |
468.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{6} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.942653879$ |
1.370845538 |
\( -\frac{26993975}{202176} a - \frac{181549561}{50544} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 7 a - 19\) , \( 29 a - 64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-19\right){x}+29a-64$ |
| 468.1-d2 |
468.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{12} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.942653879$ |
1.370845538 |
\( \frac{7218745488379}{6141096} a + \frac{113416945845413}{6141096} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 127 a - 339\) , \( 1373 a - 3024\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(127a-339\right){x}+1373a-3024$ |
| 468.1-e1 |
468.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{32} \cdot 3^{10} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.103764375$ |
1.166958512 |
\( -\frac{822656953}{207028224} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 685\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-19{x}+685$ |
| 468.1-e2 |
468.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{50} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.131485273$ |
1.166958512 |
\( -\frac{85141233386191020242827949}{316099301935480148826} a + \frac{393086913767225171255457229}{632198603870960297652} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 10760 a - 16039\) , \( 528536 a - 1327919\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(10760a-16039\right){x}+528536a-1327919$ |
| 468.1-e3 |
468.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{40} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.525941093$ |
1.166958512 |
\( \frac{1416134368422073}{725251155408} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2339\) , \( -15747\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2339{x}-15747$ |
| 468.1-e4 |
468.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{16} \cdot 3^{20} \cdot 13^{4} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$2.103764375$ |
1.166958512 |
\( \frac{242702053576633}{2554695936} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1299\) , \( 17325\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1299{x}+17325$ |
| 468.1-e5 |
468.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{50} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.131485273$ |
1.166958512 |
\( \frac{85141233386191020242827949}{316099301935480148826} a + \frac{74268148998281043589933777}{210732867956986765884} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -10760 a - 5279\) , \( -528536 a - 799383\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-10760a-5279\right){x}-528536a-799383$ |
| 468.1-e6 |
468.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{10} \cdot 13^{8} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.103764375$ |
1.166958512 |
\( \frac{986551739719628473}{111045168} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -20739\) , \( 1140957\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-20739{x}+1140957$ |
| 468.1-f1 |
468.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{2} \cdot 3^{17} \cdot 13^{4} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.121607637$ |
$4.018944894$ |
2.168808513 |
\( -\frac{7269976942057}{14549791698} a + \frac{2790187636384}{2424965283} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 9 a - 20\) , \( 45 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a-20\right){x}+45a+18$ |
| 468.1-f2 |
468.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{5} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.121607637$ |
$16.07577957$ |
2.168808513 |
\( \frac{10910603}{16848} a + \frac{1154141}{1404} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}-a$ |
| 468.1-f3 |
468.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{10} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.060803818$ |
$16.07577957$ |
2.168808513 |
\( -\frac{9005501747}{341172} a + \frac{13026853165}{113724} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a - 20\) , \( 3 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-20\right){x}+3a+24$ |
| 468.1-f4 |
468.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{2} \cdot 3^{8} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.121607637$ |
$16.07577957$ |
2.168808513 |
\( -\frac{3728428935841}{702} a + \frac{15838343223088}{1053} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -11 a - 340\) , \( 137 a + 2206\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-340\right){x}+137a+2206$ |
| 468.1-g1 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{24} \cdot 3^{5} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( -\frac{542092739}{89856} a - \frac{931208329}{159744} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( a - 24\) , \( -16 a - 12\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(a-24\right){x}-16a-12$ |
| 468.1-g2 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{7} \cdot 13^{3} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( -\frac{12474776946521}{1971216} a + \frac{7182472369115}{492804} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 130 a + 166\) , \( -300 a - 394\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(130a+166\right){x}-300a-394$ |
| 468.1-g3 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{14} \cdot 13^{6} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( -\frac{4879813408027}{4670303508} a + \frac{19623787167007}{4670303508} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 112 a - 271\) , \( 789 a - 1840\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(112a-271\right){x}+789a-1840$ |
| 468.1-g4 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{20} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( -\frac{5329029126891668773}{13817466} a + \frac{16362078318983380973}{18423288} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 1441 a - 3664\) , \( -44104 a + 99052\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1441a-3664\right){x}-44104a+99052$ |
| 468.1-g5 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{2} \cdot 3^{28} \cdot 13^{3} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( \frac{3728957993280250657}{95461183330578} a + \frac{2998114252175531956}{47730591665289} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 502 a - 1311\) , \( -8259 a + 19584\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(502a-1311\right){x}-8259a+19584$ |
| 468.1-g6 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{2} \cdot 3^{7} \cdot 13^{12} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.683867782$ |
0.758683186 |
\( \frac{1092614702272471}{7037487522} a + \frac{713185551454588}{3518743761} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -278 a + 449\) , \( 3933 a - 10336\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-278a+449\right){x}+3933a-10336$ |
| 468.1-g7 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{10} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.735471131$ |
0.758683186 |
\( \frac{8774349664979}{75816} a + \frac{30721251516415}{202176} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( a - 344\) , \( -1360 a + 564\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(a-344\right){x}-1360a+564$ |
| 468.1-g8 |
468.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{6} \cdot 3^{5} \cdot 13^{4} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.683867782$ |
0.758683186 |
\( \frac{443211926632839962731}{9126} a + \frac{256624755719786440223}{4056} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -1439 a - 2144\) , \( -44632 a - 54660\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1439a-2144\right){x}-44632a-54660$ |
| 468.1-h1 |
468.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{8} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.325820637$ |
1.754466974 |
\( \frac{3791431}{113724} a - \frac{8600395}{113724} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -3\) , \( 5 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-3{x}+5a-12$ |
| 468.1-h2 |
468.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{2} \cdot 3^{16} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.325820637$ |
1.754466974 |
\( -\frac{10534622164511}{124357194} a + \frac{14482215533296}{62178597} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 30 a - 83\) , \( 175 a - 396\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a-83\right){x}+175a-396$ |
| 468.1-i1 |
468.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{8} \cdot 13^{2} \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.325820637$ |
1.754466974 |
\( -\frac{3791431}{113724} a - \frac{400747}{9477} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -2 a - 2\) , \( -6 a - 7\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2a-2\right){x}-6a-7$ |
| 468.1-i2 |
468.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
468.1 |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{2} \cdot 3^{16} \cdot 13 \) |
$1.49855$ |
$(-a), (-a+1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.325820637$ |
1.754466974 |
\( \frac{10534622164511}{124357194} a + \frac{6143269634027}{41452398} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -32 a - 52\) , \( -176 a - 221\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-32a-52\right){x}-176a-221$ |
*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.
