| 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 |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$0.95048$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.059560260 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 5\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+5{x}+3$ |
| 400.1-a1 |
400.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.13031$ |
$(a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.722205338$ |
$2.996888981$ |
1.530440152 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( -6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+4{x}-6$ |
| 5000.1-c1 |
5000.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5000.1 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{20} \) |
$2.12533$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.599377796$ |
1.695296417 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 83\) , \( 491\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+83{x}+491$ |
| 10000.1-e1 |
10000.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10000.1 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{20} \) |
$2.52746$ |
$(a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.445334919$ |
$0.599377796$ |
4.900542221 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 82\) , \( -572\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+82{x}-572$ |
| 16200.3-a1 |
16200.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16200.3 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{8} \) |
$2.85143$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.170940323$ |
$0.998962993$ |
3.863926898 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 31\) , \( -129\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+31{x}-129$ |
| 25600.1-e1 |
25600.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{8} \) |
$3.19701$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.264839765$ |
$1.059560260$ |
3.790584357 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -26\) , \( 68 a\bigr] \) |
${y}^2={x}^{3}-26{x}+68a$ |
| 25600.1-f1 |
25600.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{8} \) |
$3.19701$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.264839765$ |
$1.059560260$ |
3.790584357 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -26\) , \( -68 a\bigr] \) |
${y}^2={x}^{3}-26{x}-68a$ |
| 32400.3-m1 |
32400.3-m |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{8} \) |
$3.39094$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.500528594$ |
$0.998962993$ |
5.656962216 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 30\) , \( 100\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+30{x}+100$ |
*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.
