| 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 |
| 1584.2-b3 |
1584.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1584.2 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{2} \) |
$1.86971$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$4.037938580$ |
3.652452872 |
\( \frac{131072}{99} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+3{x}$ |
| 14256.3-a2 |
14256.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{8} \cdot 3^{16} \cdot 11^{2} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.311641691$ |
$1.345979526$ |
3.035350913 |
\( \frac{131072}{99} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24\) , \( 25\bigr] \) |
${y}^2={x}^{3}+24{x}+25$ |
| 25344.2-i2 |
25344.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25344.2 |
\( 2^{8} \cdot 3^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{2} \) |
$3.73942$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.241129219$ |
$4.037938580$ |
5.457079236 |
\( \frac{131072}{99} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+3{x}$ |
| 39600.4-c2 |
39600.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
39600.4 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 11^{2} \) |
$4.18079$ |
$(-a), (a-1), (-a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.805821031$ |
2.177902108 |
\( \frac{131072}{99} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 9 a - 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-6\right){x}$ |
| 39600.6-b2 |
39600.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
39600.6 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 11^{2} \) |
$4.18079$ |
$(-a), (a-1), (a-2), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.805821031$ |
2.177902108 |
\( \frac{131072}{99} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a + 2\) , \( 8 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+2\right){x}+8a-2$ |
*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.
