| 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 |
| 196.2-d4 |
196.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{12} \) |
$2.08802$ |
$(2,a), (2,a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$1.313125702$ |
2.523220734 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -320\) , \( 1883\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-320{x}+1883$ |
| 98.2-b4 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.313125702$ |
2.185173255 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -32\) , \( 104\bigr] \) |
${y}^2+a{x}{y}={x}^3-32{x}+104$ |
| 28.1-a4 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 5^{12} \cdot 7^{12} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$1.313125702$ |
1.651835715 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 107 a + 684\) , \( -1330 a + 6108\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(107a+684\right){x}-1330a+6108$ |
| 98.2-a4 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{12} \) |
$2.86722$ |
$(2,a), (7,a+3), (7,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.313125702$ |
1.545150826 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -128\) , \( 832\bigr] \) |
${y}^2+a{x}{y}={x}^3-128{x}+832$ |
| 98.1-f4 |
98.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{-65}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 5^{12} \cdot 7^{12} \) |
$4.53348$ |
$(2,a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$0.342423535$ |
$1.313125702$ |
4.015556372 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -800\) , \( 13000\bigr] \) |
${y}^2+a{x}{y}={x}^3-800{x}+13000$ |
| 98.1-c4 |
98.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-78}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{12} \) |
$4.96618$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$0.580676632$ |
$1.313125702$ |
6.216212419 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6003\) , \( -147239\bigr] \) |
${y}^2+{x}{y}={x}^3-6003{x}-147239$ |
| 28.2-c4 |
28.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-455}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{12} \) |
$4.38464$ |
$(2,a), (2,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3^{2} \) |
$1.250832530$ |
$1.313125702$ |
5.544115479 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6003\) , \( -147239\bigr] \) |
${y}^2+{x}{y}={x}^3-6003{x}-147239$ |
| 98.1-c4 |
98.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{12} \) |
$6.41131$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1.269734141$ |
$2.626251405$ |
10.52882530 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6003\) , \( -147239\bigr] \) |
${y}^2+{x}{y}={x}^3-6003{x}-147239$ |
| 14.1-c4 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{12} \) |
$4.66376$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
1.168024235 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6003\) , \( -147239\bigr] \) |
${y}^2+{x}{y}={x}^3-6003{x}-147239$ |
| 98.1-e4 |
98.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-221}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{12} \) |
$8.35932$ |
$(2,a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$0.843987537$ |
$2.626251405$ |
5.367582097 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6003\) , \( -147239\bigr] \) |
${y}^2+{x}{y}={x}^3-6003{x}-147239$ |
| 14.1-e4 |
14.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-273}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{12} \) |
$5.71192$ |
$(2,a+1), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
3.814751180 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6003\) , \( -147239\bigr] \) |
${y}^2+{x}{y}={x}^3-6003{x}-147239$ |
| 196.1-b4 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$1.20552$ |
$(2), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.544398851 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-b4 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{12} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
4.382326219 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 64468 a - 292112\) , \( 14828552 a - 67190080\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(64468a-292112\right){x}+14828552a-67190080$ |
*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.
