| 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 |
| 22.1-a1 |
22.1-a |
$12$ |
$24$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{4} \cdot 11^{2} \) |
$6.92994$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1596.650924$ |
0.841626760 |
\( -\frac{201814041699}{1936} a^{3} + \frac{35160513793}{1936} a^{2} + \frac{418144402265}{968} a + \frac{488783259193}{1936} \) |
\( \bigl[a^{3} - 3 a - 1\) , \( -a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} - 2 a^{2} + 4 a + 4\) , \( -a^{3} + 4 a\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{3}-2a^{2}+4a+4\right){x}-a^{3}+4a$ |
| 176.2-f2 |
176.2-f |
$12$ |
$24$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
176.2 |
\( 2^{4} \cdot 11 \) |
\( 2^{16} \cdot 11^{2} \) |
$8.98702$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$0.337675340$ |
$777.5542742$ |
2.491220239 |
\( -\frac{201814041699}{1936} a^{3} + \frac{35160513793}{1936} a^{2} + \frac{418144402265}{968} a + \frac{488783259193}{1936} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( -15 a^{3} + 28 a^{2} + 38 a - 55\) , \( a^{3} - 7 a^{2} + a + 20\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-15a^{3}+28a^{2}+38a-55\right){x}+a^{3}-7a^{2}+a+20$ |
| 242.1-e7 |
242.1-e |
$12$ |
$24$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
242.1 |
\( 2 \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{8} \) |
$9.35198$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$150.6498514$ |
2.858780215 |
\( -\frac{201814041699}{1936} a^{3} + \frac{35160513793}{1936} a^{2} + \frac{418144402265}{968} a + \frac{488783259193}{1936} \) |
\( \bigl[1\) , \( -a^{3} + 5 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 4 a^{3} - 18 a^{2} + 3 a + 12\) , \( -25 a^{3} + 55 a^{2} + 9 a - 30\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(4a^{3}-18a^{2}+3a+12\right){x}-25a^{3}+55a^{2}+9a-30$ |
| 704.3-d7 |
704.3-d |
$12$ |
$24$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( 2^{22} \cdot 11^{2} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$0.646418137$ |
$140.1041048$ |
3.437213027 |
\( -\frac{201814041699}{1936} a^{3} + \frac{35160513793}{1936} a^{2} + \frac{418144402265}{968} a + \frac{488783259193}{1936} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 3 a\) , \( 0\) , \( 3 a^{3} - 5 a^{2} - 6 a - 1\) , \( 7 a^{3} - 9 a^{2} - 17 a - 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(3a^{3}-5a^{2}-6a-1\right){x}+7a^{3}-9a^{2}-17a-5$ |
| 704.3-q3 |
704.3-q |
$12$ |
$24$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
704.3 |
\( 2^{6} \cdot 11 \) |
\( 2^{22} \cdot 11^{2} \) |
$10.68742$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$215.4278911$ |
2.044014604 |
\( -\frac{201814041699}{1936} a^{3} + \frac{35160513793}{1936} a^{2} + \frac{418144402265}{968} a + \frac{488783259193}{1936} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( a\) , \( -8 a^{3} + 16 a^{2} + 18 a - 28\) , \( 3 a^{3} - 2 a^{2} - 12 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+a-2\right){x}^{2}+\left(-8a^{3}+16a^{2}+18a-28\right){x}+3a^{3}-2a^{2}-12a-1$ |
*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.
