| 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-a6 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$0.45564$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.142260539$ |
0.316806072 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 28 a - 27\) , \( 51 a - 158\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(28a-27\right){x}+51a-158$ |
| 36.2-a6 |
36.2-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{6} \) |
$0.78920$ |
$(-a), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$0.759892509$ |
1.053781309 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 87 a + 6\) , \( 358 a + 111\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(87a+6\right){x}+358a+111$ |
| 36.3-a6 |
36.3-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{6} \) |
$0.78920$ |
$(-a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$6.839032582$ |
1.053781309 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 114 a - 191\) , \( -670 a + 1528\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(114a-191\right){x}-670a+1528$ |
| 256.1-c6 |
256.1-c |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{34} \) |
$1.28875$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$3.412266367$ |
1.892784823 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 456 a - 432\) , \( -2400 a + 9188\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(456a-432\right){x}-2400a+9188$ |
| 256.1-d6 |
256.1-d |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{34} \) |
$1.28875$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$2.532039089$ |
$0.329043108$ |
1.848593902 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1896 a + 2376\) , \( 36680 a + 47444\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1896a+2376\right){x}+36680a+47444$ |
| 256.1-f6 |
256.1-f |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{34} \) |
$1.28875$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.281337676$ |
$2.961387977$ |
1.848593902 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1896 a + 2376\) , \( -36680 a - 47444\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1896a+2376\right){x}-36680a-47444$ |
| 324.1-a6 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 256 a - 243\) , \( -1141 a + 3997\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(256a-243\right){x}-1141a+3997$ |
| 676.1-d6 |
676.1-d |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 13^{6} \) |
$1.64285$ |
$(-2a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.092209650$ |
$3.785569646$ |
1.936270087 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1540 a + 1930\) , \( 24220 a + 31792\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1540a+1930\right){x}+24220a+31792$ |
| 1156.2-b6 |
1156.2-b |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1156.2 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 17^{6} \) |
$1.87867$ |
$(a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$3.310384624$ |
0.918135500 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 784 a - 1526\) , \( -13814 a + 33114\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(784a-1526\right){x}-13814a+33114$ |
| 1156.3-b6 |
1156.3-b |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1156.3 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 17^{6} \) |
$1.87867$ |
$(a+4), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$3.310384624$ |
0.918135500 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 556 a + 258\) , \( 3332 a + 8420\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(556a+258\right){x}+3332a+8420$ |
*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.
