| 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-a4 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.313125702$ |
0.505422318 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -36 a + 35\) , \( -70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-36a+35\right){x}-70$ |
| 9604.3-c4 |
9604.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9604.3 |
\( 2^{2} \cdot 7^{4} \) |
\( 2^{6} \cdot 7^{24} \) |
$1.53219$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.187589386$ |
2.599314781 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1740{x}+22184$ |
| 12348.2-a4 |
12348.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{18} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \) |
$0.879052894$ |
$0.286547520$ |
2.326864094 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -852 a + 532\) , \( -4185 a + 7742\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-852a+532\right){x}-4185a+7742$ |
| 12348.3-a4 |
12348.3-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{18} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \) |
$0.879052894$ |
$0.286547520$ |
2.326864094 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -533 a + 852\) , \( 4185 a + 3557\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-533a+852\right){x}+4185a+3557$ |
| 12544.2-k4 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{12} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \) |
$1.052334262$ |
$0.328281425$ |
3.191239339 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -568\) , \( 4464\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-568{x}+4464$ |
| 33124.4-c4 |
33124.4-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.4 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.364195542$ |
2.523220734 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -249 a - 284\) , \( -2511 a - 1186\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-249a-284\right){x}-2511a-1186$ |
| 33124.6-c4 |
33124.6-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.6 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (4a-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.364195542$ |
2.523220734 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 284 a + 248\) , \( 2511 a - 3697\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(284a+248\right){x}+2511a-3697$ |
| 87808.2-a4 |
87808.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{30} \cdot 7^{18} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{5} \) |
$1.119693107$ |
$0.124078716$ |
2.566762269 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1705 a + 4547\) , \( -77511 a - 2759\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1705a+4547\right){x}-77511a-2759$ |
| 87808.2-r4 |
87808.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{30} \cdot 7^{18} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.124078716$ |
3.438570245 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2842 a - 1705\) , \( 77511 a + 2759\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2842a-1705\right){x}+77511a+2759$ |
| 87808.3-c4 |
87808.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{30} \cdot 7^{18} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{5} \) |
$1.119693107$ |
$0.124078716$ |
2.566762269 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1705 a + 2842\) , \( 77511 a - 80270\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1705a+2842\right){x}+77511a-80270$ |
| 87808.3-t4 |
87808.3-t |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{30} \cdot 7^{18} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.124078716$ |
3.438570245 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4547 a + 1705\) , \( -77511 a + 80270\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4547a+1705\right){x}-77511a+80270$ |
| 112896.2-r4 |
112896.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 3^{6} \cdot 7^{12} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.189533369$ |
2.626251405 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1705\) , \( -25079 a + 13392\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1705\right){x}-25079a+13392$ |
| 112896.2-ba4 |
112896.2-ba |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 3^{6} \cdot 7^{12} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.189533369$ |
2.626251405 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1704 a\) , \( 26784 a - 13392\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-1704a{x}+26784a-13392$ |
| 122500.2-e4 |
122500.2-e |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
122500.2 |
\( 2^{2} \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{6} \cdot 5^{12} \cdot 7^{12} \) |
$2.89556$ |
$(-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.262625140$ |
3.639040694 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -887 a + 887\) , \( -7831\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-887a+887\right){x}-7831$ |
*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.
