| 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 |
| 7056.1-CMa1 |
7056.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 7^{4} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$1.682188720$ |
1.942424221 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 12 a - 32\bigr] \) |
${y}^2={x}^{3}+12a-32$ |
| 7056.1-a1 |
7056.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{7} \cdot 7^{3} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.053036440$ |
$2.840841185$ |
2.087718508 |
\( -\frac{256}{3} a - \frac{256}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 1\) , \( 8 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+1\right){x}+8a-6$ |
| 7056.1-a2 |
7056.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{20} \cdot 7^{9} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.742510171$ |
$0.202917227$ |
2.087718508 |
\( -\frac{547472}{2187} a + \frac{48160}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 748 a + 556\) , \( -6928 a + 3384\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(748a+556\right){x}-6928a+3384$ |
| 7056.1-a3 |
7056.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{3} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.106072881$ |
$1.420420592$ |
2.087718508 |
\( \frac{53296}{3} a - 3360 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 28 a - 44\) , \( 80 a - 72\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a-44\right){x}+80a-72$ |
| 7056.1-a4 |
7056.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{13} \cdot 7^{9} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.371255085$ |
$0.405834455$ |
2.087718508 |
\( -\frac{47028992}{81} a + \frac{48771328}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 478 a + 541\) , \( -9172 a + 11034\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(478a+541\right){x}-9172a+11034$ |
| 7056.1-b1 |
7056.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 7^{8} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.589507626$ |
1.361409547 |
\( -\frac{452304}{49} a - \frac{118800}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -228 a + 69\) , \( -1248 a + 1074\bigr] \) |
${y}^2={x}^{3}+\left(-228a+69\right){x}-1248a+1074$ |
| 7056.1-b2 |
7056.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 7^{7} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.179015253$ |
1.361409547 |
\( \frac{20736}{7} a - \frac{13824}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -33 a + 39\) , \( -51 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(-33a+39\right){x}-51a-60$ |
| 7056.1-b3 |
7056.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{3} \cdot 7^{12} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.589507626$ |
1.361409547 |
\( \frac{4757232}{117649} a + \frac{223153968}{117649} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 149 a - 19\) , \( 33 a - 220\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(149a-19\right){x}+33a-220$ |
| 7056.1-b4 |
7056.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{9} \) |
$1.41853$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.179015253$ |
1.361409547 |
\( -\frac{3512064}{343} a + \frac{36883968}{343} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 84 a - 9\) , \( 98 a + 211\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(84a-9\right){x}+98a+211$ |
*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.
