| 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 |
| 288.1-a5 |
288.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.32818$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$3.147871475$ |
$6.870412800$ |
3.419556851 |
\( \frac{8323073360}{6561} a + \frac{26331470648}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 56 a - 181\) , \( 123 a - 390\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(56a-181\right){x}+123a-390$ |
| 288.1-b5 |
288.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$2.32818$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$6.870412800$ |
2.172615291 |
\( \frac{8323073360}{6561} a + \frac{26331470648}{6561} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 15 a - 42\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a-42\right){x}$ |
| 288.1-s5 |
288.1-s |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.32818$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$18.09482301$ |
1.430521364 |
\( \frac{8323073360}{6561} a + \frac{26331470648}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 56 a - 181\) , \( -123 a + 390\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(56a-181\right){x}-123a+390$ |
| 288.1-t5 |
288.1-t |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$2.32818$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.471045986$ |
$18.09482301$ |
4.208725423 |
\( \frac{8323073360}{6561} a + \frac{26331470648}{6561} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 13 a - 47\) , \( 14 a - 45\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-47\right){x}+14a-45$ |
*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.
