| 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 |
| 2450.2-a2 |
2450.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2450.2 |
\( 2 \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 7^{4} \) |
$1.25736$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.306970664$ |
$1.849974466$ |
2.271551562 |
\( \frac{611960049}{122500} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -17\) , \( 19\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-17{x}+19$ |
| 61250.3-a2 |
61250.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61250.3 |
\( 2 \cdot 5^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{20} \cdot 7^{4} \) |
$2.81155$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.369994893$ |
1.479979573 |
\( \frac{611960049}{122500} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -442\) , \( 2784\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-442{x}+2784$ |
| 98000.2-j2 |
98000.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.2 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{14} \cdot 7^{4} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.413666866$ |
3.309334931 |
\( \frac{611960049}{122500} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -284 i - 213\) , \( 1931 i + 512\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-284i-213\right){x}+1931i+512$ |
| 98000.3-j2 |
98000.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{14} \cdot 7^{4} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.413666866$ |
3.309334931 |
\( \frac{611960049}{122500} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 283 i - 213\) , \( -2144 i + 229\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(283i-213\right){x}-2144i+229$ |
*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.
