| 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 |
| 200.4-a1 |
200.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
200.4 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.88909$ |
$(-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.015624997$ |
$6.689230455$ |
0.632072750 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}-{x}-a$ |
| 1600.7-c1 |
1600.7-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1600.7 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$1.49526$ |
$(-a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$4.730000215$ |
3.575544077 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( a\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+a{x}-1$ |
| 5000.4-a1 |
5000.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5000.4 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$1.98806$ |
$(-a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.337846091$ |
4.045266342 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -8 a - 9\) , \( 6 a - 55\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-8a-9\right){x}+6a-55$ |
| 6400.5-d1 |
6400.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.344615227$ |
2.528291463 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 3\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-3\right){x}+a+1$ |
| 12800.4-f1 |
12800.4-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.4 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.312331464$ |
$4.730000215$ |
4.467019669 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}-a-1$ |
| 16200.4-d1 |
16200.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16200.4 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$2.66727$ |
$(-a+1), (3), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.229743485$ |
3.371055285 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -3 a - 3\) , \( -a + 11\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-3a-3\right){x}-a+11$ |
| 19600.5-d1 |
19600.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.5 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 7^{6} \) |
$2.79738$ |
$(-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.060056512$ |
$2.528291463$ |
8.103956924 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 2\) , \( -7 a + 5\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+2\right){x}-7a+5$ |
| 25600.5-b1 |
25600.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25600.5 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.99053$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$0.577386419$ |
$4.730000215$ |
4.128941187 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}+a+1$ |
| 25600.7-a1 |
25600.7-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25600.7 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{2} \) |
$2.99053$ |
$(a), (-a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.365000107$ |
1.787772038 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+a+5$ |
| 40000.7-a1 |
40000.7-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.7 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{14} \cdot 5^{14} \) |
$3.34351$ |
$(-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.417855700$ |
$0.946000043$ |
2.390498359 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 25 a - 8\) , \( 43 a - 144\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(25a-8\right){x}+43a-144$ |
| 48400.13-a1 |
48400.13-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.13 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 11^{6} \) |
$3.50670$ |
$(-a+1), (-2a+3), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.016878868$ |
1.524617117 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 6 a - 6\) , \( -6 a - 6\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-6\right){x}-6a-6$ |
| 48400.15-c1 |
48400.15-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.15 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 11^{6} \) |
$3.50670$ |
$(-a+1), (2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.016878868$ |
1.524617117 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -3 a + 8\) , \( -4 a + 13\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-3a+8\right){x}-4a+13$ |
*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.
