| 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 |
| 11552.2-a1 |
11552.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{2} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.071171000$ |
$5.963775842$ |
2.401039863 |
\( \frac{27000}{19} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+3{x}$ |
| 11552.2-b1 |
11552.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$0.319679844$ |
$4.296507316$ |
3.884863868 |
\( \frac{64}{19} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-{x}+a$ |
| 11552.2-c1 |
11552.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{10} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Ns |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.029707001$ |
$0.603483608$ |
5.070716035 |
\( -\frac{4741632}{2476099} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14\) , \( 606\bigr] \) |
${y}^2={x}^{3}-14{x}+606$ |
| 11552.2-d1 |
11552.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.109359759$ |
$4.183446943$ |
5.176030150 |
\( -\frac{13824}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 2\bigr] \) |
${y}^2={x}^{3}-2{x}+2$ |
| 11552.2-e1 |
11552.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.317256616$ |
$4.183446943$ |
3.753962649 |
\( -\frac{13824}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2={x}^{3}-2{x}-2$ |
| 11552.2-f1 |
11552.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{10} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$0.603483608$ |
1.706909408 |
\( -\frac{4741632}{2476099} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14\) , \( -606\bigr] \) |
${y}^2={x}^{3}-14{x}-606$ |
| 11552.2-g1 |
11552.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$0.319679844$ |
$4.296507316$ |
3.884863868 |
\( \frac{64}{19} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1\) , \( -a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-{x}-a$ |
| 11552.2-h1 |
11552.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11552.2 |
\( 2^{5} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{2} \) |
$2.62028$ |
$(a), (-3a+1), (3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.963775842$ |
8.434052680 |
\( \frac{27000}{19} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}-1$ |
*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.
