| 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 |
| 4032.5-b1 |
4032.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.5 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{6} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.102278192$ |
$2.161678695$ |
3.008345196 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 4\) , \( -a + 7\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(8a-4\right){x}-a+7$ |
| 8064.4-a1 |
8064.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{6} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.161678695$ |
1.634075498 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 4\) , \( a - 7\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a-4\right){x}+a-7$ |
| 14112.4-b1 |
14112.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.4 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{12} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.817037749$ |
2.470489938 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -54 a + 23\) , \( 36 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-54a+23\right){x}+36a+4$ |
| 16128.7-b1 |
16128.7-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.7 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{6} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.528537664$ |
1.155465865 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a + 19\) , \( 3 a\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-12a+19\right){x}+3a$ |
| 32256.4-n1 |
32256.4-n |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
32256.4 |
\( 2^{9} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{6} \) |
$3.16840$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.169117628$ |
$1.528537664$ |
4.689831522 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a - 9\) , \( 7 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-9\right){x}+7a-7$ |
| 36288.5-d1 |
36288.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.5 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{12} \cdot 3^{14} \cdot 7^{6} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.841932339$ |
$0.720559565$ |
5.503124027 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 69 a - 30\) , \( -11 a - 49\bigr] \) |
${y}^2={x}^{3}+\left(69a-30\right){x}-11a-49$ |
*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.
