| 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 |
| 7056.3-CMa1 |
7056.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 7^{4} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$1.682188720$ |
1.942424221 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -12 a - 20\bigr] \) |
${y}^2={x}^{3}-12a-20$ |
| 7056.3-a1 |
7056.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{7} \cdot 7^{3} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.053036440$ |
$2.840841185$ |
2.087718508 |
\( \frac{256}{3} a - \frac{512}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( -5 a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-2\right){x}-5a$ |
| 7056.3-a2 |
7056.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{20} \cdot 7^{9} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.742510171$ |
$0.202917227$ |
2.087718508 |
\( \frac{547472}{2187} a + \frac{3353488}{2187} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -746 a + 1303\) , \( 6181 a - 2241\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-746a+1303\right){x}+6181a-2241$ |
| 7056.3-a3 |
7056.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{3} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.106072881$ |
$1.420420592$ |
2.087718508 |
\( -\frac{53296}{3} a + \frac{43216}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -26 a - 17\) , \( -107 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-26a-17\right){x}-107a-9$ |
| 7056.3-a4 |
7056.3-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{13} \cdot 7^{9} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.371255085$ |
$0.405834455$ |
2.087718508 |
\( \frac{47028992}{81} a + \frac{1742336}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -476 a + 1018\) , \( 8695 a + 2880\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-476a+1018\right){x}+8695a+2880$ |
| 7056.3-b1 |
7056.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 7^{8} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.589507626$ |
1.361409547 |
\( \frac{452304}{49} a - \frac{571104}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 228 a - 159\) , \( 1248 a - 174\bigr] \) |
${y}^2={x}^{3}+\left(228a-159\right){x}+1248a-174$ |
| 7056.3-b2 |
7056.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 7^{7} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.179015253$ |
1.361409547 |
\( -\frac{20736}{7} a + \frac{6912}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 33 a + 6\) , \( 51 a - 111\bigr] \) |
${y}^2={x}^{3}+\left(33a+6\right){x}+51a-111$ |
| 7056.3-b3 |
7056.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{3} \cdot 7^{12} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.589507626$ |
1.361409547 |
\( -\frac{4757232}{117649} a + \frac{227911200}{117649} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -147 a + 129\) , \( 115 a - 316\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-147a+129\right){x}+115a-316$ |
| 7056.3-b4 |
7056.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{9} \) |
$1.41853$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.179015253$ |
1.361409547 |
\( \frac{3512064}{343} a + \frac{33371904}{343} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -82 a + 74\) , \( -15 a + 235\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-82a+74\right){x}-15a+235$ |
*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.
