| 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-b2 |
8450.6-b |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.6 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 5^{7} \cdot 13^{8} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.539539763$ |
1.079079527 |
\( -\frac{2944910839}{500000} a + \frac{24766677}{500000} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 104 i - 185\) , \( 952 i - 732\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(104i-185\right){x}+952i-732$ |
| 42250.6-j2 |
42250.6-j |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{9} \cdot 5^{13} \cdot 13^{2} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$0.016059424$ |
$0.869981728$ |
6.035647390 |
\( -\frac{2944910839}{500000} a + \frac{24766677}{500000} \) |
\( \bigl[i\) , \( i\) , \( 1\) , \( -57 i + 59\) , \( 107 i + 292\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-57i+59\right){x}+107i+292$ |
| 42250.9-d2 |
42250.9-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{9} \cdot 5^{13} \cdot 13^{2} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$0.869981728$ |
1.739963456 |
\( -\frac{2944910839}{500000} a + \frac{24766677}{500000} \) |
\( \bigl[1\) , \( -i + 1\) , \( 1\) , \( -42 i - 71\) , \( -169 i - 275\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-42i-71\right){x}-169i-275$ |
| 67600.6-b2 |
67600.6-b |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{21} \cdot 5^{7} \cdot 13^{2} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.517809331$ |
$0.972669141$ |
4.029257268 |
\( -\frac{2944910839}{500000} a + \frac{24766677}{500000} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -67 i - 8\) , \( -168 i + 129\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-67i-8\right){x}-168i+129$ |
*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.
