| 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 |
| 10108.3-a1 |
10108.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10108.3 |
\( 2^{2} \cdot 7 \cdot 19^{2} \) |
\( 2^{24} \cdot 7^{3} \cdot 19^{4} \) |
$1.55191$ |
$(-3a+1), (-5a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.089997492$ |
$0.781840464$ |
1.949975534 |
\( -\frac{646862543}{702464} a + \frac{3391232917}{1404928} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 64 a + 27\) , \( 214 a - 197\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(64a+27\right){x}+214a-197$ |
| 10108.3-a2 |
10108.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10108.3 |
\( 2^{2} \cdot 7 \cdot 19^{2} \) |
\( 2^{8} \cdot 7 \cdot 19^{4} \) |
$1.55191$ |
$(-3a+1), (-5a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.269992477$ |
$2.345521394$ |
1.949975534 |
\( -\frac{3579687}{112} a + \frac{1752629}{112} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -16 a + 2\) , \( 15 a - 11\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-16a+2\right){x}+15a-11$ |
| 10108.3-b1 |
10108.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10108.3 |
\( 2^{2} \cdot 7 \cdot 19^{2} \) |
\( 2^{12} \cdot 7 \cdot 19^{2} \) |
$1.55191$ |
$(-3a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.056205220$ |
$3.255106227$ |
2.535084471 |
\( \frac{1127925}{224} a - \frac{4599531}{448} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -6 a - 1\) , \( 5 a\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-6a-1\right){x}+5a$ |
| 10108.3-b2 |
10108.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10108.3 |
\( 2^{2} \cdot 7 \cdot 19^{2} \) |
\( 2^{4} \cdot 7^{3} \cdot 19^{2} \) |
$1.55191$ |
$(-3a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$0.168615660$ |
$3.255106227$ |
2.535084471 |
\( -\frac{108852903}{1372} a + \frac{26567325}{1372} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -5 a - 7\) , \( -5 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-7\right){x}-5a-5$ |
| 10108.3-c1 |
10108.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10108.3 |
\( 2^{2} \cdot 7 \cdot 19^{2} \) |
\( 2^{2} \cdot 7 \cdot 19^{9} \) |
$1.55191$ |
$(-3a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.484619355$ |
$1.150841738$ |
2.575999177 |
\( -\frac{1646}{7} a + \frac{13915}{14} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -27 a - 5\) , \( -a + 58\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-27a-5\right){x}-a+58$ |
*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.
