| 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 |
| 1521.3-a1 |
1521.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{3} \cdot 13^{9} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.793858490$ |
2.104454048 |
\( -\frac{13457741}{169} a + \frac{30927116}{169} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 25 a - 67\) , \( 114 a - 231\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-67\right){x}+114a-231$ |
| 1521.3-a2 |
1521.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{7} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.793858490$ |
2.104454048 |
\( -\frac{46343}{13} a + \frac{110915}{13} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 54 a - 108\) , \( -239 a + 560\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(54a-108\right){x}-239a+560$ |
| 1521.3-a3 |
1521.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.793858490$ |
2.104454048 |
\( -\frac{555810959}{13} a + \frac{1279993418}{13} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 769 a - 1798\) , \( -15930 a + 36531\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(769a-1798\right){x}-15930a+36531$ |
| 1521.3-a4 |
1521.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{3} \cdot 13^{12} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.793858490$ |
2.104454048 |
\( \frac{525219013}{2197} a + \frac{688038953}{2197} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -40 a - 197\) , \( 439 a + 575\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-40a-197\right){x}+439a+575$ |
| 1521.3-b1 |
1521.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 13^{4} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.358246808$ |
$12.47124223$ |
3.304373272 |
\( \frac{1173836521}{27} a - \frac{901104113}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 17 a - 81\) , \( -74 a + 263\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(17a-81\right){x}-74a+263$ |
| 1521.3-b2 |
1521.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{15} \cdot 13^{4} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.119415602$ |
$4.157080746$ |
3.304373272 |
\( \frac{9799933}{19683} a + \frac{3654118}{6561} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 24 a + 30\) , \( -27 a - 31\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(24a+30\right){x}-27a-31$ |
| 1521.3-c1 |
1521.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{9} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$2.595296036$ |
0.719805610 |
\( -\frac{1790960}{27} a + \frac{780949}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 603 a - 1409\) , \( 10954 a - 25209\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(603a-1409\right){x}+10954a-25209$ |
| 1521.3-c2 |
1521.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{12} \cdot 13^{9} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \) |
$1$ |
$1.297648018$ |
0.719805610 |
\( \frac{899953417066}{729} a + \frac{390812454469}{243} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 148 a - 759\) , \( 23980 a - 52509\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(148a-759\right){x}+23980a-52509$ |
| 1521.3-d1 |
1521.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 13^{10} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$9.033575589$ |
$0.198099307$ |
3.970644012 |
\( \frac{1173836521}{27} a - \frac{901104113}{9} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1465 a - 2031\) , \( -45323 a - 59637\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1465a-2031\right){x}-45323a-59637$ |
| 1521.3-d2 |
1521.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{15} \cdot 13^{10} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$3.011191863$ |
$0.594297923$ |
3.970644012 |
\( \frac{9799933}{19683} a + \frac{3654118}{6561} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 109 a - 151\) , \( 2445 a - 5570\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(109a-151\right){x}+2445a-5570$ |
| 1521.3-e1 |
1521.3-e |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{2} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B, 19B.8.2 |
$1$ |
\( 2 \) |
$2.647505990$ |
$0.845750829$ |
2.484092131 |
\( -3387888351672962316333 a - 4413658407915562663495 \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 11089 a - 28807\) , \( 985507 a - 2197839\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(11089a-28807\right){x}+985507a-2197839$ |
| 1521.3-e2 |
1521.3-e |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{2} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B, 19B.8.2 |
$1$ |
\( 2 \) |
$7.942517970$ |
$0.281916943$ |
2.484092131 |
\( 3387888351672962316333 a - 7801546759588524979828 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1005 a - 11530\) , \( 288310 a - 27456\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1005a-11530\right){x}+288310a-27456$ |
| 1521.3-e3 |
1521.3-e |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{2} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B, 19B.8.1 |
$1$ |
\( 2 \) |
$0.418027261$ |
$5.356421921$ |
2.484092131 |
\( -17787 a - 21988 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5 a - 5\) , \( -5 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a-5\right){x}-5a-6$ |
| 1521.3-e4 |
1521.3-e |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{2} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B, 19B.8.1 |
$1$ |
\( 2 \) |
$0.139342420$ |
$16.06926576$ |
2.484092131 |
\( 17787 a - 39775 \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 8 a + 10\) , \( 3 a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+10\right){x}+3a+4$ |
| 1521.3-f1 |
1521.3-f |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{13} \cdot 13^{2} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \) |
$0.223076517$ |
$2.743343882$ |
1.357851941 |
\( -\frac{219992945997349946}{2187} a - \frac{95533816840246301}{729} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 917 a - 2176\) , \( 33701 a - 77399\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(917a-2176\right){x}+33701a-77399$ |
| 1521.3-f2 |
1521.3-f |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{7} \cdot 13^{2} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \) |
$0.031868073$ |
$19.20340718$ |
1.357851941 |
\( \frac{7918}{3} a - 6017 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( a\) , \( 2 a + 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+a{x}+2a+3$ |
| 1521.3-g1 |
1521.3-g |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{9} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.379853549$ |
1.214752811 |
\( -\frac{13457741}{169} a + \frac{30927116}{169} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 142 a - 343\) , \( -1266 a + 2985\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(142a-343\right){x}-1266a+2985$ |
| 1521.3-g2 |
1521.3-g |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{3} \cdot 13^{7} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.379853549$ |
1.214752811 |
\( -\frac{46343}{13} a + \frac{110915}{13} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 12 a - 18\) , \( 21 a - 44\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-18\right){x}+21a-44$ |
| 1521.3-g3 |
1521.3-g |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{3} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.189926774$ |
1.214752811 |
\( -\frac{555810959}{13} a + \frac{1279993418}{13} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 142 a - 343\) , \( 1282 a - 3021\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(142a-343\right){x}+1282a-3021$ |
| 1521.3-g4 |
1521.3-g |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 13^{12} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.189926774$ |
1.214752811 |
\( \frac{525219013}{2197} a + \frac{688038953}{2197} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 77 a - 668\) , \( 983 a + 1243\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(77a-668\right){x}+983a+1243$ |
| 1521.3-h1 |
1521.3-h |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B.1.2, 19B.8.2 |
$1$ |
\( 2 \cdot 3 \) |
$7.347799970$ |
$0.078189691$ |
1.912125514 |
\( -3387888351672962316333 a - 4413658407915562663495 \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -114376 a - 200554\) , \( -34887776 a - 40972752\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-114376a-200554\right){x}-34887776a-40972752$ |
| 1521.3-h2 |
1521.3-h |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B.1.1, 19B.8.2 |
$1$ |
\( 2 \cdot 3 \) |
$22.04339991$ |
$0.234569075$ |
1.912125514 |
\( 3387888351672962316333 a - 7801546759588524979828 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 397446 a - 931733\) , \( -186348516 a + 428300775\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(397446a-931733\right){x}-186348516a+428300775$ |
| 1521.3-h3 |
1521.3-h |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B.1.1, 19B.8.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.160178942$ |
$4.456812436$ |
1.912125514 |
\( -17787 a - 21988 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -29 a + 42\) , \( 49 a - 85\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-29a+42\right){x}+49a-85$ |
| 1521.3-h4 |
1521.3-h |
$4$ |
$57$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 19$ |
3B.1.2, 19B.8.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.386726314$ |
$1.485604145$ |
1.912125514 |
\( 17787 a - 39775 \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 24 a - 29\) , \( 64 a - 132\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(24a-29\right){x}+64a-132$ |
| 1521.3-i1 |
1521.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{11} \cdot 13^{7} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.228884036$ |
$2.926253491$ |
3.989432881 |
\( -\frac{7611584}{3159} a + \frac{6398965}{1053} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 38 a - 74\) , \( 160 a - 345\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(38a-74\right){x}+160a-345$ |
| 1521.3-i2 |
1521.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.457768073$ |
$2.926253491$ |
3.989432881 |
\( -\frac{479646368}{767637} a + \frac{1577111371}{255879} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 103 a - 334\) , \( -776 a + 2112\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(103a-334\right){x}-776a+2112$ |
| 1521.3-i3 |
1521.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{26} \cdot 13^{7} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.915536146$ |
$0.731563372$ |
3.989432881 |
\( \frac{180699527638714}{45328197213} a + \frac{82902964902913}{15109399071} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -352 a + 316\) , \( -6262 a + 10601\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-352a+316\right){x}-6262a+10601$ |
| 1521.3-i4 |
1521.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{11} \cdot 13^{10} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.228884036$ |
$2.926253491$ |
3.989432881 |
\( -\frac{262161428182}{41067} a + \frac{412575307241}{13689} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 1598 a - 5144\) , \( -58314 a + 156331\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(1598a-5144\right){x}-58314a+156331$ |
| 1521.3-j1 |
1521.3-j |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{13} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.342880276$ |
$0.169912640$ |
2.649813753 |
\( -\frac{219992945997349946}{2187} a - \frac{95533816840246301}{729} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1325 a - 5743\) , \( -132890 a - 16526\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1325a-5743\right){x}-132890a-16526$ |
| 1521.3-j2 |
1521.3-j |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{7} \cdot 13^{8} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.334697182$ |
$1.189388481$ |
2.649813753 |
\( \frac{7918}{3} a - 6017 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 40 a - 88\) , \( 178 a - 419\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(40a-88\right){x}+178a-419$ |
| 1521.3-k1 |
1521.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{3} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$5.078710624$ |
1.408580889 |
\( -\frac{1790960}{27} a + \frac{780949}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -3 a - 19\) , \( -17 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3a-19\right){x}-17a-6$ |
| 1521.3-k2 |
1521.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{12} \cdot 13^{3} \) |
$2.01207$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \) |
$1$ |
$2.539355312$ |
1.408580889 |
\( \frac{899953417066}{729} a + \frac{390812454469}{243} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -98 a - 134\) , \( -744 a - 923\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-98a-134\right){x}-744a-923$ |
*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.
