| 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 |
| 19208.1-a1 |
19208.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{4} \) |
$2.97546$ |
$(a), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.117127913$ |
$3.701446717$ |
2.452488037 |
\( 48384 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 7\bigr] \) |
${y}^2={x}^{3}-7{x}+7$ |
| 19208.1-b1 |
19208.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{14} \) |
$2.97546$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.844493815$ |
$0.913677040$ |
2.182399124 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -174\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-4{x}-174$ |
| 19208.1-b2 |
19208.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{10} \cdot 7^{16} \) |
$2.97546$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.688987630$ |
$0.456838520$ |
2.182399124 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -494\) , \( -4094\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-494{x}-4094$ |
| 19208.1-c1 |
19208.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{8} \) |
$2.97546$ |
$(a), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.071541228$ |
$2.124947498$ |
2.579887928 |
\( 12544 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -16\) , \( 29\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-16{x}+29$ |
| 19208.1-d1 |
19208.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{4} \cdot 7^{14} \) |
$2.97546$ |
$(a), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.657265035$ |
$1.147513062$ |
5.935114063 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 14\) , \( 80\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+14{x}+80$ |
| 19208.1-d2 |
19208.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{10} \cdot 7^{20} \) |
$2.97546$ |
$(a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.657265035$ |
$0.286878265$ |
5.935114063 |
\( \frac{11090466}{2401} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -721\) , \( -5555\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-721{x}-5555$ |
| 19208.1-d3 |
19208.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{16} \) |
$2.97546$ |
$(a), (7)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.657265035$ |
$0.573756531$ |
5.935114063 |
\( \frac{740772}{49} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -231\) , \( 1403\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-231{x}+1403$ |
| 19208.1-d4 |
19208.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{10} \cdot 7^{14} \) |
$2.97546$ |
$(a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.657265035$ |
$0.286878265$ |
5.935114063 |
\( \frac{1443468546}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -3661\) , \( 87153\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-3661{x}+87153$ |
| 19208.1-e1 |
19208.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{20} \) |
$2.97546$ |
$(a), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$3.883135787$ |
$0.303563928$ |
6.668186390 |
\( 12544 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -800\) , \( -8359\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-800{x}-8359$ |
| 19208.1-f1 |
19208.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{16} \) |
$2.97546$ |
$(a), (7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cn |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$0.528778102$ |
8.973661968 |
\( 48384 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -343\) , \( -2401\bigr] \) |
${y}^2={x}^{3}-343{x}-2401$ |
*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.
