| 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 |
| 40000.4-a1 |
40000.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{6} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.293211026$ |
$3.843711527$ |
3.407783938 |
\( 2048 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-2$ |
| 40000.4-a2 |
40000.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{16} \cdot 5^{6} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.146605513$ |
$1.921855763$ |
3.407783938 |
\( 78608 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -28\) , \( 48\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-28{x}+48$ |
| 40000.4-b1 |
40000.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{22} \cdot 5^{4} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.480241903$ |
$2.286542514$ |
5.117088715 |
\( 270 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5\) , \( -10\bigr] \) |
${y}^2={x}^{3}+5{x}-10$ |
| 40000.4-c1 |
40000.4-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{18} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.832699559$ |
$0.768742305$ |
4.260033598 |
\( 2048 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -83\) , \( -88\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-83{x}-88$ |
| 40000.4-c2 |
40000.4-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{16} \cdot 5^{18} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.665399119$ |
$0.384371152$ |
4.260033598 |
\( 78608 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -708\) , \( 7412\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-708{x}+7412$ |
| 40000.4-d1 |
40000.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{22} \cdot 5^{16} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3 \) |
$2.865675827$ |
$0.457308502$ |
5.943859878 |
\( 270 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 125\) , \( -1250\bigr] \) |
${y}^2={x}^{3}+125{x}-1250$ |
| 40000.4-e1 |
40000.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{20} \cdot 5^{20} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.156731320$ |
$0.299688898$ |
5.721096022 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 325\) , \( -4250\bigr] \) |
${y}^2={x}^{3}+325{x}-4250$ |
| 40000.4-e2 |
40000.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{16} \cdot 5^{16} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.578365660$ |
$0.599377796$ |
5.721096022 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -175\) , \( -750\bigr] \) |
${y}^2={x}^{3}-175{x}-750$ |
| 40000.4-e3 |
40000.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.156731320$ |
$1.198755592$ |
5.721096022 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \) |
${y}^2={x}^{3}-50{x}+125$ |
| 40000.4-e4 |
40000.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
40000.4 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{20} \cdot 5^{14} \) |
$3.34351$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.156731320$ |
$0.299688898$ |
5.721096022 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2675\) , \( -53250\bigr] \) |
${y}^2={x}^{3}-2675{x}-53250$ |
*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.
