| 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 |
| 2880.4-c4 |
2880.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2880.4 |
\( 2^{6} \cdot 3^{2} \cdot 5 \) |
\( 2^{16} \cdot 3^{5} \cdot 5^{4} \) |
$2.17112$ |
$(-a), (a-1), (a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.322634104$ |
1.595156748 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 49 a - 48\) , \( 153 a + 36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(49a-48\right){x}+153a+36$ |
| 11520.4-ba4 |
11520.4-ba |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
11520.4 |
\( 2^{8} \cdot 3^{2} \cdot 5 \) |
\( 2^{16} \cdot 3^{5} \cdot 5^{4} \) |
$3.07042$ |
$(-a), (a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.322634104$ |
4.785470245 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 49 a - 48\) , \( -153 a - 36\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(49a-48\right){x}-153a-36$ |
| 14400.6-j4 |
14400.6-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.6 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{5} \cdot 5^{10} \) |
$3.24658$ |
$(-a), (a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.551656790$ |
$0.591499953$ |
4.427657523 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 48 a + 392\) , \( -1780 a + 1976\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(48a+392\right){x}-1780a+1976$ |
| 25920.6-e4 |
25920.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25920.6 |
\( 2^{6} \cdot 3^{4} \cdot 5 \) |
\( 2^{16} \cdot 3^{17} \cdot 5^{4} \) |
$3.76048$ |
$(-a), (a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.462279456$ |
$0.440878034$ |
3.932843707 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 441 a - 435\) , \( -4572 a - 538\bigr] \) |
${y}^2={x}^{3}+\left(441a-435\right){x}-4572a-538$ |
| 34560.4-s4 |
34560.4-s |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.4 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{16} \cdot 3^{11} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.763623156$ |
0.920964178 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -146 a - 3\) , \( -837 a + 810\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-146a-3\right){x}-837a+810$ |
| 34560.4-bz4 |
34560.4-bz |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.4 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{16} \cdot 3^{11} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.704258208$ |
$0.763623156$ |
7.783158984 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -146 a - 3\) , \( 837 a - 810\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-146a-3\right){x}+837a-810$ |
| 34560.6-h4 |
34560.6-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.6 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{16} \cdot 3^{11} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.051310059$ |
$0.763623156$ |
3.872875619 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -99 a + 243\) , \( -387 a - 1098\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-99a+243\right){x}-387a-1098$ |
| 34560.6-bj4 |
34560.6-bj |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.6 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{16} \cdot 3^{11} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.763623156$ |
1.841928356 |
\( \frac{4735750624}{16875} a + \frac{648744976}{1875} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -99 a + 243\) , \( 387 a + 1098\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-99a+243\right){x}+387a+1098$ |
*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.
