| 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 |
| 4.1-a5 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$0.45564$ |
$(2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Cs, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$28.55651349$ |
0.316806072 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 3\) , \( -a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+3{x}-a+4$ |
| 36.2-a5 |
36.2-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$0.78920$ |
$(-a), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs.1.1, 5B.4.1 |
$1$ |
\( 3 \) |
$1$ |
$11.39838763$ |
1.053781309 |
\( \frac{1331}{8} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -a + 3\) , \( -3 a + 7\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+3\right){x}-3a+7$ |
| 36.3-a5 |
36.3-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$0.78920$ |
$(-a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs.1.1, 5B.4.1 |
$1$ |
\( 3 \) |
$1$ |
$11.39838763$ |
1.053781309 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a + 2\) , \( 3 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(a+2\right){x}+3a+4$ |
| 256.1-c5 |
256.1-c |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$1.28875$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$3.412266367$ |
1.892784823 |
\( \frac{1331}{8} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a + 26\) , \( 79 a - 182\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-11a+26\right){x}+79a-182$ |
| 256.1-d5 |
256.1-d |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$1.28875$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.168802605$ |
$4.935646628$ |
1.848593902 |
\( \frac{1331}{8} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -3 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-3a+4$ |
| 256.1-f5 |
256.1-f |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$1.28875$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.168802605$ |
$4.935646628$ |
1.848593902 |
\( \frac{1331}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 3 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+3a-4$ |
| 324.1-a5 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 15\) , \( 37 a - 85\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-6a+15\right){x}+37a-85$ |
| 676.1-d5 |
676.1-d |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$1.64285$ |
$(-2a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.153682750$ |
$3.785569646$ |
1.936270087 |
\( \frac{1331}{8} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3\) , \( -5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3{x}-5$ |
| 1156.2-b5 |
1156.2-b |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1156.2 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{6} \) |
$1.87867$ |
$(a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$3.310384624$ |
0.918135500 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 4 a + 8\) , \( -23 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+8\right){x}-23a-30$ |
| 1156.3-b5 |
1156.3-b |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1156.3 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{6} \) |
$1.87867$ |
$(a+4), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$3.310384624$ |
0.918135500 |
\( \frac{1331}{8} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -5 a + 13\) , \( 23 a - 53\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-5a+13\right){x}+23a-53$ |
*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.
