| 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 |
| 11.1-a1 |
11.1-a |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{8} \) |
$6.35478$ |
$(-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$120.9845885$ |
1.147921305 |
\( -\frac{1271382434328458944}{214358881} a^{3} + \frac{3189239753697071944}{214358881} a^{2} + \frac{274621437566108395}{214358881} a - \frac{1685647152341252737}{214358881} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -1\) , \( a^{3} - 4 a\) , \( 5 a^{3} - 14 a^{2} + 3 a + 1\) , \( -16 a^{3} + 40 a^{2} - 7 a - 14\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-{x}^{2}+\left(5a^{3}-14a^{2}+3a+1\right){x}-16a^{3}+40a^{2}-7a-14$ |
| 121.1-a3 |
121.1-a |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{14} \) |
$8.57580$ |
$(-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.485008180$ |
$46.29203171$ |
1.704226669 |
\( -\frac{1271382434328458944}{214358881} a^{3} + \frac{3189239753697071944}{214358881} a^{2} + \frac{274621437566108395}{214358881} a - \frac{1685647152341252737}{214358881} \) |
\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a^{3} - 4 a - 1\) , \( 105 a^{3} - 261 a^{2} - 17 a + 133\) , \( 1159 a^{3} - 2880 a^{2} - 269 a + 1530\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(105a^{3}-261a^{2}-17a+133\right){x}+1159a^{3}-2880a^{2}-269a+1530$ |
| 176.2-h1 |
176.2-h |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
176.2 |
\( 2^{4} \cdot 11 \) |
\( - 2^{12} \cdot 11^{8} \) |
$8.98702$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.423839095$ |
$11.43699257$ |
2.472149892 |
\( -\frac{1271382434328458944}{214358881} a^{3} + \frac{3189239753697071944}{214358881} a^{2} + \frac{274621437566108395}{214358881} a - \frac{1685647152341252737}{214358881} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 3 a\) , \( 11 a^{3} + 3 a^{2} - 53 a - 46\) , \( 41 a^{3} + 5 a^{2} - 173 a - 131\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(11a^{3}+3a^{2}-53a-46\right){x}+41a^{3}+5a^{2}-173a-131$ |
| 704.3-h3 |
704.3-h |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{18} \cdot 11^{8} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.026092759$ |
$211.8085177$ |
3.356027195 |
\( -\frac{1271382434328458944}{214358881} a^{3} + \frac{3189239753697071944}{214358881} a^{2} + \frac{274621437566108395}{214358881} a - \frac{1685647152341252737}{214358881} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{2} - 2\) , \( 31 a^{3} - 73 a^{2} - 10 a + 33\) , \( -154 a^{3} + 393 a^{2} + 20 a - 190\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(31a^{3}-73a^{2}-10a+33\right){x}-154a^{3}+393a^{2}+20a-190$ |
| 704.3-m6 |
704.3-m |
$6$ |
$8$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( - 2^{18} \cdot 11^{8} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$14.01996619$ |
2.128379236 |
\( -\frac{1271382434328458944}{214358881} a^{3} + \frac{3189239753697071944}{214358881} a^{2} + \frac{274621437566108395}{214358881} a - \frac{1685647152341252737}{214358881} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( 13 a^{3} - 3 a^{2} - 47 a - 21\) , \( -61 a^{3} - 24 a^{2} + 166 a + 94\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(13a^{3}-3a^{2}-47a-21\right){x}-61a^{3}-24a^{2}+166a+94$ |
*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.
