| 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 |
| 9408.2-c6 |
9408.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9408.2 |
\( 2^{6} \cdot 3 \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 7^{3} \) |
$1.52431$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.051909001$ |
$0.433723891$ |
2.055279100 |
\( -\frac{1359217262594}{147} a + \frac{2174322882812}{147} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2688 a - 1792\) , \( -44704 a + 300\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2688a-1792\right){x}-44704a+300$ |
| 37632.2-k6 |
37632.2-k |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 7^{3} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.433723891$ |
2.003284843 |
\( -\frac{1359217262594}{147} a + \frac{2174322882812}{147} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -896 a + 2688\) , \( 44704 a - 300\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-896a+2688\right){x}+44704a-300$ |
| 112896.2-h6 |
112896.2-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 7^{3} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.250410605$ |
2.313194086 |
\( -\frac{1359217262594}{147} a + \frac{2174322882812}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5376 a + 2688\) , \( -132312 a + 267324\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5376a+2688\right){x}-132312a+267324$ |
| 112896.2-be6 |
112896.2-be |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 7^{3} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1.052410681$ |
$0.250410605$ |
4.868860331 |
\( -\frac{1359217262594}{147} a + \frac{2174322882812}{147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8062 a + 5375\) , \( 124249 a - 261949\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-8062a+5375\right){x}+124249a-261949$ |
*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.
