| 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 |
| 8281.5-a2 |
8281.5-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8281.5 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$1.47645$ |
$(-3a+1), (3a-2), (-4a+1), (4a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$0.117693898$ |
$0.486651176$ |
1.190456688 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -117 a + 117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-117a+117\right){x}-1245$ |
| 8281.2-b2 |
8281.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8281.2 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$1.70486$ |
$(-3a-2), (2a+3), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$0.126609754$ |
$0.486651176$ |
2.218132294 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
| 1183.1-b2 |
1183.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$1.38654$ |
$(-2a+1), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
1.558673681 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
| 8281.1-b2 |
8281.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8281.1 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$2.41104$ |
$(7), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
0.729002861 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
| 8281.1-a2 |
8281.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8281.1 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$2.82719$ |
$(7), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
0.621695729 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
| 8281.2-a2 |
8281.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
8281.2 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$3.71566$ |
$(-a-1), (a-2), (13)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{4} \) |
$0.046650276$ |
$0.486651176$ |
3.374972266 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 637.1-b2 |
637.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
637.1 |
\( 7^{2} \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$2.80353$ |
$(13,a+6), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
0.660346558 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 8281.2-a2 |
8281.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
8281.2 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$5.58976$ |
$(a+1), (a-2), (7)$ |
$1 \le r \le 2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
|
\( 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
8.102483316 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 637.2-c2 |
637.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
637.2 |
\( 7^{2} \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$3.23724$ |
$(7,a+1), (7,a+6), (a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.070956840$ |
$0.486651176$ |
6.206051506 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 8281.1-a2 |
8281.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
8281.1 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$6.97745$ |
$(7), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
1.007620087 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 91.1-a2 |
91.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
0.864596597 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 637.2-b2 |
637.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
637.2 |
\( 7^{2} \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$4.57815$ |
$(7,a+3), (7,a+4), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.036714234$ |
$0.486651176$ |
2.270599754 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 91.1-c2 |
91.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-455}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$5.88714$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
0.386659352 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 91.1-d2 |
91.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$7.44671$ |
$(7,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 2^{2} \cdot 3^{2} \) |
$0.117693898$ |
$0.973302352$ |
2.751129525 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 637.1-b2 |
637.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
637.1 |
\( 7^{2} \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$1.61862$ |
$(-2a+1), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.147409310$ |
$0.450314296$ |
1.325566344 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
| 1183.1-e2 |
1183.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.243054316$ |
$0.450314296$ |
1.719657357 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
*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.
