| 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-c1 |
8450.6-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.6 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{7} \cdot 5^{7} \cdot 13^{2} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 7 \) |
$0.011180466$ |
$2.341190353$ |
3.664584158 |
\( -\frac{2255889}{50000} a + \frac{83040173}{50000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 8 i - 1\) , \( i - 2\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(8i-1\right){x}+i-2$ |
| 42250.6-c1 |
42250.6-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{7} \cdot 5^{13} \cdot 13^{8} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.422685994$ |
$0.290388924$ |
2.945839946 |
\( -\frac{2255889}{50000} a + \frac{83040173}{50000} \) |
\( \bigl[1\) , \( i + 1\) , \( i\) , \( 310 i + 459\) , \( -749 i - 313\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(310i+459\right){x}-749i-313$ |
| 42250.9-g1 |
42250.9-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{7} \cdot 5^{13} \cdot 13^{8} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$0.290388924$ |
4.065444937 |
\( -\frac{2255889}{50000} a + \frac{83040173}{50000} \) |
\( \bigl[1\) , \( i\) , \( 1\) , \( -527 i + 168\) , \( -1094 i + 177\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-527i+168\right){x}-1094i+177$ |
| 67600.6-h1 |
67600.6-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{19} \cdot 5^{7} \cdot 13^{8} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.062746849$ |
$0.324664687$ |
4.889204672 |
\( -\frac{2255889}{50000} a + \frac{83040173}{50000} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -145 i + 418\) , \( 10 i + 989\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-145i+418\right){x}+10i+989$ |
*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.
