| 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 |
| 8450.6-a2 |
8450.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.6 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2 \cdot 5^{3} \cdot 13^{4} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.388736433$ |
$3.658969912$ |
1.896499887 |
\( \frac{40729}{50} a + \frac{80613}{50} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -3\) , \( i\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-3{x}+i$ |
| 42250.6-g2 |
42250.6-g |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2 \cdot 5^{9} \cdot 13^{10} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.453839361$ |
3.630714895 |
\( \frac{40729}{50} a + \frac{80613}{50} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( 197 i - 116\) , \( -779 i + 478\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(197i-116\right){x}-779i+478$ |
| 42250.9-c2 |
42250.9-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2 \cdot 5^{9} \cdot 13^{10} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$0.453839361$ |
0.907678723 |
\( \frac{40729}{50} a + \frac{80613}{50} \) |
\( \bigl[1\) , \( -i + 1\) , \( i\) , \( 55 i + 222\) , \( 439 i - 643\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(55i+222\right){x}+439i-643$ |
| 67600.6-e2 |
67600.6-e |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{3} \cdot 13^{10} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.507407832$ |
2.029631328 |
\( \frac{40729}{50} a + \frac{80613}{50} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 167 i + 70\) , \( -490 i - 549\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(167i+70\right){x}-490i-549$ |
*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.
