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-a10 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
0.505422318 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
9604.3-c10 |
9604.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9604.3 |
\( 2^{2} \cdot 7^{4} \) |
\( 2^{18} \cdot 7^{16} \) |
$1.53219$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.062529795$ |
2.599314781 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 133795 a\) , \( 18781197\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+133795a{x}+18781197$ |
12348.2-a10 |
12348.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{10} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$2.637158682$ |
$0.095515840$ |
2.326864094 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -65532 a + 40957\) , \( -3308745 a + 6121178\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-65532a+40957\right){x}-3308745a+6121178$ |
12348.3-a10 |
12348.3-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{10} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$2.637158682$ |
$0.095515840$ |
2.326864094 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -40958 a + 65532\) , \( 3308745 a + 2812433\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-40958a+65532\right){x}+3308745a+2812433$ |
12544.2-k10 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{42} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$3.157002788$ |
$0.109427141$ |
3.191239339 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -43688\) , \( 3529328\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-43688{x}+3529328$ |
33124.4-c10 |
33124.4-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.4 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{3} \) |
$1$ |
$0.121398514$ |
2.523220734 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -19114 a - 21844\) , \( -1985247 a - 937478\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-19114a-21844\right){x}-1985247a-937478$ |
33124.6-c10 |
33124.6-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33124.6 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 13^{6} \) |
$2.08802$ |
$(-3a+1), (3a-2), (4a-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{3} \) |
$1$ |
$0.121398514$ |
2.523220734 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 21844 a + 19113\) , \( 1985247 a - 2922725\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(21844a+19113\right){x}+1985247a-2922725$ |
87808.2-a10 |
87808.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{42} \cdot 7^{10} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.359079322$ |
$0.041359572$ |
2.566762269 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -131065 a + 349507\) , \( -63309463 a - 3398263\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-131065a+349507\right){x}-63309463a-3398263$ |
87808.2-r10 |
87808.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{42} \cdot 7^{10} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{5} \) |
$1$ |
$0.041359572$ |
3.438570245 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -218442 a - 131065\) , \( 63309463 a + 3398263\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-218442a-131065\right){x}+63309463a+3398263$ |
87808.3-c10 |
87808.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{42} \cdot 7^{10} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.359079322$ |
$0.041359572$ |
2.566762269 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 131065 a + 218442\) , \( 63309463 a - 66707726\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(131065a+218442\right){x}+63309463a-66707726$ |
87808.3-t10 |
87808.3-t |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{42} \cdot 7^{10} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{5} \) |
$1$ |
$0.041359572$ |
3.438570245 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -349507 a + 131065\) , \( -63309463 a + 66707726\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-349507a+131065\right){x}-63309463a+66707726$ |
112896.2-r10 |
112896.2-r |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{42} \cdot 3^{6} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.063177789$ |
2.626251405 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 131065\) , \( -21044903 a + 10587984\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+131065\right){x}-21044903a+10587984$ |
112896.2-ba10 |
112896.2-ba |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{42} \cdot 3^{6} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$9$ |
\( 2^{4} \) |
$1$ |
$0.063177789$ |
2.626251405 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -131064 a\) , \( 21175968 a - 10587984\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-131064a{x}+21175968a-10587984$ |
122500.2-e10 |
122500.2-e |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
122500.2 |
\( 2^{2} \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 5^{12} \cdot 7^{4} \) |
$2.89556$ |
$(-3a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.087541713$ |
3.639040694 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -68262 a + 68262\) , \( -6824956\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-68262a+68262\right){x}-6824956$ |
*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.