| 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 |
| 6400.5-a1 |
6400.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.070515942$ |
1.213850982 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-36{x}+140$ |
| 6400.5-a2 |
6400.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$3.211547828$ |
1.213850982 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+4{x}-4$ |
| 6400.5-a3 |
6400.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$6.423095656$ |
1.213850982 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 6400.5-a4 |
6400.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$2.141031885$ |
1.213850982 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 6400.5-b1 |
6400.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.498444490$ |
1.132717564 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \) |
${y}^2={x}^{3}+13{x}+34$ |
| 6400.5-b2 |
6400.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.132717564 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 6400.5-b3 |
6400.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.993777963$ |
1.132717564 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \) |
${y}^2={x}^{3}-2{x}-1$ |
| 6400.5-b4 |
6400.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.498444490$ |
1.132717564 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \) |
${y}^2={x}^{3}-107{x}+426$ |
| 6400.5-c1 |
6400.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
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 |
\( \frac{1024}{5} a + \frac{1024}{5} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 2\) , \( -a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-2\right){x}-a+2$ |
| 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 |
\( -\frac{1024}{5} a + \frac{2048}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 3\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-3\right){x}+a+1$ |
*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.
