| 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 |
| 5202.1-a1 |
5202.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.1 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{7} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (-2a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.035586375$ |
$3.063864834$ |
2.467109039 |
\( -\frac{3575}{24} a + \frac{96797}{24} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -4 a - 5\) , \( 3 a - 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-5\right){x}+3a-1$ |
| 5202.1-b1 |
5202.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.1 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{7} \cdot 17^{8} \) |
$2.14648$ |
$(a), (-a-1), (-2a+3)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.743096372$ |
2.101793936 |
\( -\frac{3575}{24} a + \frac{96797}{24} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 55 a - 68\) , \( -228 a + 72\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(55a-68\right){x}-228a+72$ |
| 15606.7-d1 |
15606.7-d |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15606.7 |
\( 2 \cdot 3^{3} \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{7} \cdot 17^{8} \) |
$2.82492$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.743096372$ |
2.101793936 |
\( -\frac{3575}{24} a + \frac{96797}{24} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -73 a + 4\) , \( 120 a - 178\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-73a+4\right){x}+120a-178$ |
| 15606.7-g1 |
15606.7-g |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15606.7 |
\( 2 \cdot 3^{3} \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{7} \cdot 17^{2} \) |
$2.82492$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.114186624$ |
$3.063864834$ |
5.937191811 |
\( -\frac{3575}{24} a + \frac{96797}{24} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -a + 6\) , \( -2 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-a+6\right){x}-2a-3$ |
| 41616.1-f1 |
41616.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.1 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{7} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.590753253$ |
$0.371548186$ |
7.449849637 |
\( -\frac{3575}{24} a + \frac{96797}{24} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 222 a - 276\) , \( -1824 a + 572\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(222a-276\right){x}-1824a+572$ |
| 41616.1-g1 |
41616.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.1 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{7} \cdot 17^{2} \) |
$3.60993$ |
$(a), (-a-1), (-2a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.531932417$ |
4.332959202 |
\( -\frac{3575}{24} a + \frac{96797}{24} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -11 a - 19\) , \( 16 a + 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-11a-19\right){x}+16a+31$ |
*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.
