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 |
1521.1-a1 |
1521.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{12} \cdot 13^{2} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.029525360$ |
$9.070696649$ |
2.971147155 |
\( \frac{19394657}{59049} a + \frac{7881788}{19683} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( a + 1\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+1\right){x}+5$ |
1521.1-b1 |
1521.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{2} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B |
$1$ |
\( 1 \) |
$1$ |
$2.634676907$ |
0.730727898 |
\( -\frac{238419968}{27} a - \frac{310607872}{27} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 2 a - 5\) , \( 42 a - 97\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(2a-5\right){x}+42a-97$ |
1521.1-b2 |
1521.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{28} \cdot 13^{2} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B |
$1$ |
\( 1 \) |
$1$ |
$2.634676907$ |
0.730727898 |
\( -\frac{470646624944128}{10460353203} a - \frac{201905494589440}{3486784401} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -186 a + 375\) , \( -1854 a + 4439\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-186a+375\right){x}-1854a+4439$ |
1521.1-b3 |
1521.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{2} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B |
$1$ |
\( 1 \) |
$1$ |
$2.634676907$ |
0.730727898 |
\( \frac{238419968}{27} a - \frac{183009280}{9} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -2 a - 3\) , \( -42 a - 55\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}-42a-55$ |
1521.1-b4 |
1521.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{28} \cdot 13^{2} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B |
$1$ |
\( 1 \) |
$1$ |
$2.634676907$ |
0.730727898 |
\( \frac{470646624944128}{10460353203} a - \frac{1076363108712448}{10460353203} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 186 a + 189\) , \( 1854 a + 2585\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(186a+189\right){x}+1854a+2585$ |
1521.1-c1 |
1521.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{12} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.095726637$ |
$1.117405975$ |
3.560027593 |
\( -\frac{19394657}{59049} a + \frac{43040021}{59049} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -52 a - 61\) , \( -2133 a - 2785\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-52a-61\right){x}-2133a-2785$ |
1521.1-d1 |
1521.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 13^{14} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.637942791$ |
$0.993853719$ |
2.908547464 |
\( -\frac{676845982849}{187388721} a - \frac{558092735498}{187388721} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1229 a + 2715\) , \( -1452 a + 3897\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1229a+2715\right){x}-1452a+3897$ |
1521.1-d2 |
1521.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{7} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.318971395$ |
$0.993853719$ |
2.908547464 |
\( -\frac{1710800841881825}{85293} a + \frac{1313196835851943}{28431} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 273 a + 259\) , \( 12158 a + 15386\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(273a+259\right){x}+12158a+15386$ |
1521.1-d3 |
1521.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{3} \cdot 13^{7} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.318971395$ |
$3.975414877$ |
2.908547464 |
\( \frac{173165}{117} a + \frac{24023}{13} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 6 a - 15\) , \( 69 a - 159\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-15\right){x}+69a-159$ |
1521.1-d4 |
1521.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.659485697$ |
$3.975414877$ |
2.908547464 |
\( -\frac{75022925}{1053} a + \frac{62074228}{351} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 201 a - 470\) , \( 2292 a - 5268\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(201a-470\right){x}+2292a-5268$ |
1521.1-d5 |
1521.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{10} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.318971395$ |
$3.975414877$ |
2.908547464 |
\( \frac{548869002845}{13689} a + \frac{715076828719}{13689} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 266 a - 730\) , \( 329 a - 224\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(266a-730\right){x}+329a-224$ |
1521.1-d6 |
1521.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{3} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.659485697$ |
$3.975414877$ |
2.908547464 |
\( \frac{678199424037617413}{117} a + \frac{883541687195951426}{117} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 2801 a - 8335\) , \( -127942 a + 326791\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2801a-8335\right){x}-127942a+326791$ |
1521.1-e1 |
1521.1-e |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{10} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.498435896$ |
2.211859914 |
\( -\frac{658489}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 392 a - 910\) , \( 5912 a - 13643\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(392a-910\right){x}+5912a-13643$ |
1521.1-e2 |
1521.1-e |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{28} \cdot 13^{10} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.498435896$ |
2.211859914 |
\( -\frac{276301129}{4782969} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2927 a - 6825\) , \( -649808 a + 1498062\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2927a-6825\right){x}-649808a+1498062$ |
1521.1-f1 |
1521.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{10} \cdot 13^{7} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.900243086$ |
1.608765409 |
\( -\frac{29458043467457294458}{85293} a + \frac{67835264831664798469}{85293} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2257 a - 4266\) , \( 109977 a + 161531\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2257a-4266\right){x}+109977a+161531$ |
1521.1-f2 |
1521.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.800486172$ |
1.608765409 |
\( \frac{12167}{39} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -18 a + 45\) , \( -133 a + 309\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-18a+45\right){x}-133a+309$ |
1521.1-f3 |
1521.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{10} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.800486172$ |
1.608765409 |
\( \frac{10218313}{1521} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 177 a - 410\) , \( -1433 a + 3299\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(177a-410\right){x}-1433a+3299$ |
1521.1-f4 |
1521.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 13^{14} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.450121543$ |
1.608765409 |
\( \frac{822656953}{85683} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 762 a - 1775\) , \( 14323 a - 33049\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(762a-1775\right){x}+14323a-33049$ |
1521.1-f5 |
1521.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.800486172$ |
1.608765409 |
\( \frac{37159393753}{1053} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 2712 a - 6325\) , \( -103509 a + 238547\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(2712a-6325\right){x}-103509a+238547$ |
1521.1-f6 |
1521.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{10} \cdot 13^{7} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.900243086$ |
1.608765409 |
\( \frac{29458043467457294458}{85293} a + \frac{12792407121402501337}{28431} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 2257 a - 6520\) , \( -107721 a + 264989\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(2257a-6520\right){x}-107721a+264989$ |
1521.1-g1 |
1521.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.2.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.008228643$ |
$22.88420607$ |
2.506880609 |
\( -\frac{658489}{9} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}+8$ |
1521.1-g2 |
1521.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{28} \cdot 13^{4} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.2.3 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.403203524$ |
$0.467024613$ |
2.506880609 |
\( -\frac{276301129}{4782969} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -75\) , \( -1422\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-75{x}-1422$ |
1521.1-h1 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.576390951$ |
0.991912381 |
\( -\frac{24125}{27} a - \frac{1375}{27} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -11 a - 13\) , \( -55 a - 71\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-11a-13\right){x}-55a-71$ |
1521.1-h2 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{26} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.788195475$ |
0.991912381 |
\( -\frac{1794398270320625}{282429536481} a + \frac{1272952673786125}{94143178827} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 1312 a - 3083\) , \( -33562 a + 77613\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1312a-3083\right){x}-33562a+77613$ |
1521.1-h3 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{14} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.788195475$ |
0.991912381 |
\( -\frac{16961124145384625}{6561} a + \frac{13019221158502750}{2187} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 899 a + 52\) , \( -14940 a - 5427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(899a+52\right){x}-14940a-5427$ |
1521.1-h4 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.576390951$ |
0.991912381 |
\( \frac{24125}{27} a - \frac{8500}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 12 a - 28\) , \( 43 a - 101\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a-28\right){x}+43a-101$ |
1521.1-h5 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.576390951$ |
0.991912381 |
\( -\frac{1567304375}{729} a + \frac{1203684625}{243} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -163 a - 218\) , \( 828 a + 1070\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-163a-218\right){x}+828a+1070$ |
1521.1-h6 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.576390951$ |
0.991912381 |
\( -\frac{449577713875}{531441} a + \frac{1037190880375}{531441} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -206 a - 338\) , \( -2135 a - 2580\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-206a-338\right){x}-2135a-2580$ |
1521.1-h7 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{26} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.788195475$ |
0.991912381 |
\( \frac{1794398270320625}{282429536481} a + \frac{2024459751037750}{282429536481} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1311 a - 1768\) , \( 32250 a + 42283\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1311a-1768\right){x}+32250a+42283$ |
1521.1-h8 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.894097737$ |
0.991912381 |
\( -\frac{450190437580625}{27} a + \frac{345562524359500}{9} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1138 a - 1583\) , \( -28812 a - 37969\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1138a-1583\right){x}-28812a-37969$ |
1521.1-h9 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.576390951$ |
0.991912381 |
\( \frac{449577713875}{531441} a + \frac{195871055500}{177147} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 207 a - 548\) , \( 1928 a - 4170\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(207a-548\right){x}+1928a-4170$ |
1521.1-h10 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.576390951$ |
0.991912381 |
\( \frac{1567304375}{729} a + \frac{2043749500}{729} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 162 a - 380\) , \( -829 a + 1899\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(162a-380\right){x}-829a+1899$ |
1521.1-h11 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{14} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.788195475$ |
0.991912381 |
\( \frac{16961124145384625}{6561} a + \frac{22096539330123625}{6561} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -898 a + 947\) , \( 15838 a - 21317\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-898a+947\right){x}+15838a-21317$ |
1521.1-h12 |
1521.1-h |
$12$ |
$24$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{6} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.894097737$ |
0.991912381 |
\( \frac{450190437580625}{27} a + \frac{586497135497875}{27} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 1137 a - 2720\) , \( 28811 a - 66780\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1137a-2720\right){x}+28811a-66780$ |
1521.1-i1 |
1521.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{12} \cdot 13^{2} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.029525360$ |
$9.070696649$ |
2.971147155 |
\( -\frac{19394657}{59049} a + \frac{43040021}{59049} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -a + 4\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a+4\right){x}+a+2$ |
1521.1-j1 |
1521.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{3} \cdot 13^{7} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.318971395$ |
$3.975414877$ |
2.908547464 |
\( -\frac{173165}{117} a + \frac{389372}{117} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -6 a - 9\) , \( -69 a - 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-6a-9\right){x}-69a-90$ |
1521.1-j2 |
1521.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 13^{14} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.637942791$ |
$0.993853719$ |
2.908547464 |
\( \frac{676845982849}{187388721} a - \frac{411646239449}{62462907} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1229 a + 1486\) , \( 1452 a + 2445\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1229a+1486\right){x}+1452a+2445$ |
1521.1-j3 |
1521.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{10} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.318971395$ |
$3.975414877$ |
2.908547464 |
\( -\frac{548869002845}{13689} a + \frac{32408867476}{351} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -266 a - 464\) , \( -329 a + 105\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-266a-464\right){x}-329a+105$ |
1521.1-j4 |
1521.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.659485697$ |
$3.975414877$ |
2.908547464 |
\( \frac{75022925}{1053} a + \frac{111199759}{1053} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -201 a - 269\) , \( -2292 a - 2976\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-201a-269\right){x}-2292a-2976$ |
1521.1-j5 |
1521.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{3} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.659485697$ |
$3.975414877$ |
2.908547464 |
\( -\frac{678199424037617413}{117} a + \frac{520580370411189613}{39} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -2801 a - 5534\) , \( 127942 a + 198849\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-2801a-5534\right){x}+127942a+198849$ |
1521.1-j6 |
1521.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( - 3^{9} \cdot 13^{7} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.318971395$ |
$0.993853719$ |
2.908547464 |
\( \frac{1710800841881825}{85293} a + \frac{2228789665674004}{85293} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -274 a + 533\) , \( -12158 a + 27544\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-274a+533\right){x}-12158a+27544$ |
1521.1-k1 |
1521.1-k |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.2.1 |
$1$ |
\( 1 \) |
$1$ |
$7.365994941$ |
2.042959419 |
\( -\frac{238419968}{27} a - \frac{310607872}{27} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -26 a - 43\) , \( 65 a + 288\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-26a-43\right){x}+65a+288$ |
1521.1-k2 |
1521.1-k |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{28} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.2.3 |
$49$ |
\( 1 \) |
$1$ |
$0.150326427$ |
2.042959419 |
\( -\frac{470646624944128}{10460353203} a - \frac{201905494589440}{3486784401} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -2314 a - 2279\) , \( -67899 a - 97888\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-2314a-2279\right){x}-67899a-97888$ |
1521.1-k3 |
1521.1-k |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.2.1 |
$1$ |
\( 1 \) |
$1$ |
$7.365994941$ |
2.042959419 |
\( \frac{238419968}{27} a - \frac{183009280}{9} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 26 a - 69\) , \( -65 a + 353\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(26a-69\right){x}-65a+353$ |
1521.1-k4 |
1521.1-k |
$4$ |
$21$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{28} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.2.3 |
$49$ |
\( 1 \) |
$1$ |
$0.150326427$ |
2.042959419 |
\( \frac{470646624944128}{10460353203} a - \frac{1076363108712448}{10460353203} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 2314 a - 4593\) , \( 67899 a - 165787\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(2314a-4593\right){x}+67899a-165787$ |
1521.1-l1 |
1521.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{12} \cdot 13^{8} \) |
$2.01207$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.095726637$ |
$1.117405975$ |
3.560027593 |
\( \frac{19394657}{59049} a + \frac{7881788}{19683} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 51 a - 113\) , \( 2132 a - 4918\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(51a-113\right){x}+2132a-4918$ |
*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.