| 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 |
| 100.1-a3 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.79925$ |
$(a), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.826873828$ |
$6.423095656$ |
0.625917922 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 400.1-b3 |
400.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.13031$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$6.423095656$ |
2.270907247 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 2500.1-a3 |
2500.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2500.1 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$1.78718$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.284619131$ |
3.633451596 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 62\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-33{x}+62$ |
| 8100.3-a3 |
8100.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8100.3 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$2.39775$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.304906633$ |
$2.141031885$ |
3.951095909 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( -11\bigr] \) |
${y}^2={x}^{3}-12{x}-11$ |
| 10000.1-b3 |
10000.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10000.1 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$2.52746$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.561930274$ |
$1.284619131$ |
2.041746452 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -62\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-33{x}-62$ |
| 25600.1-c3 |
25600.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$3.19701$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.554723742$ |
$4.541814495$ |
4.993069659 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}$ |
| 25600.1-h3 |
25600.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$3.19701$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.554723742$ |
$4.541814495$ |
4.993069659 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}$ |
| 28900.1-c3 |
28900.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28900.1 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{6} \) |
$3.29540$ |
$(a), (-2a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$1.557829519$ |
2.203103634 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 16 a - 2\) , \( -16 a - 29\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(16a-2\right){x}-16a-29$ |
| 28900.3-c3 |
28900.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28900.3 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{6} \) |
$3.29540$ |
$(a), (2a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$1.557829519$ |
2.203103634 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -16 a - 2\) , \( 16 a - 29\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-16a-2\right){x}+16a-29$ |
| 32400.3-i3 |
32400.3-i |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$3.39094$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.141031885$ |
3.027876330 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( 11\bigr] \) |
${y}^2={x}^{3}-12{x}+11$ |
*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.
