| 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 |
| 12096.2-a1 |
12096.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12096.2 |
\( 2^{6} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{11} \cdot 7 \) |
$1.62315$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.165273828$ |
1.345542317 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a + 21\) , \( 72 a - 74\bigr] \) |
${y}^2={x}^{3}+\left(24a+21\right){x}+72a-74$ |
| 48384.2-a1 |
48384.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.173851334$ |
$2.018313476$ |
3.241350559 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 8\) , \( -16 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-8\right){x}-16a$ |
| 48384.2-h1 |
48384.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{5} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.066556414$ |
$2.018313476$ |
3.722709501 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 15\) , \( 9 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+15\right){x}+9a+15$ |
| 48384.2-i1 |
48384.2-i |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
48384.2 |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
\( 2^{22} \cdot 3^{11} \cdot 7 \) |
$2.29549$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.165273828$ |
2.691084634 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 45\) , \( -72 a + 74\bigr] \) |
${y}^2={x}^{3}+\left(21a-45\right){x}-72a+74$ |
| 84672.3-l1 |
84672.3-l |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
84672.3 |
\( 2^{6} \cdot 3^{3} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{5} \cdot 7^{7} \) |
$2.64018$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.762850789$ |
1.761728434 |
\( -\frac{13096}{7} a + \frac{23186}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -95 a + 85\) , \( 167 a - 360\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-95a+85\right){x}+167a-360$ |
*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.
