| 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 |
| 5202.4-a1 |
5202.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 17^{8} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.369327134$ |
1.044614883 |
\( -\frac{3805069}{559872} a - \frac{2875943}{559872} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -3 a + 67\) , \( -1506 a - 1533\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-3a+67\right){x}-1506a-1533$ |
| 5202.4-b1 |
5202.4-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{5} \cdot 3^{32} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.065563680$ |
1.390815689 |
\( \frac{811409154866127821}{1647129056757192} a - \frac{79261954805628389}{411782264189298} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -5773 a - 561\) , \( 137153 a - 442749\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5773a-561\right){x}+137153a-442749$ |
| 5202.4-b2 |
5202.4-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.655636803$ |
1.390815689 |
\( -\frac{507662}{243} a + \frac{2905757}{486} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 87 a - 86\) , \( 446 a + 48\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(87a-86\right){x}+446a+48$ |
| 5202.4-b3 |
5202.4-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{16} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.327818401$ |
1.390815689 |
\( \frac{362392621}{118098} a + \frac{474522278}{59049} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 312 a - 466\) , \( -3501 a + 3002\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(312a-466\right){x}-3501a+3002$ |
| 5202.4-b4 |
5202.4-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$0.131127360$ |
1.390815689 |
\( -\frac{105956215006891}{114791256} a + \frac{9859152651013}{459165024} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -6673 a + 959\) , \( 150309 a - 291157\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6673a+959\right){x}+150309a-291157$ |
| 5202.4-c1 |
5202.4-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{5} \cdot 3^{32} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.270325979$ |
1.911493331 |
\( \frac{811409154866127821}{1647129056757192} a - \frac{79261954805628389}{411782264189298} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -44 a + 477\) , \( -4395 a + 1929\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-44a+477\right){x}-4395a+1929$ |
| 5202.4-c2 |
5202.4-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.703259793$ |
1.911493331 |
\( -\frac{507662}{243} a + \frac{2905757}{486} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -4 a - 8\) , \( -8 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-4a-8\right){x}-8a-2$ |
| 5202.4-c3 |
5202.4-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{16} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.351629896$ |
1.911493331 |
\( \frac{362392621}{118098} a + \frac{474522278}{59049} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -19 a - 28\) , \( 41 a + 52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-19a-28\right){x}+41a+52$ |
| 5202.4-c4 |
5202.4-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.540651958$ |
1.911493331 |
\( -\frac{105956215006891}{114791256} a + \frac{9859152651013}{459165024} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 16 a + 557\) , \( -3303 a + 257\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(16a+557\right){x}-3303a+257$ |
| 5202.4-d1 |
5202.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.4 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{5} \cdot 7 \) |
$0.010099910$ |
$1.522774784$ |
4.872100372 |
\( -\frac{3805069}{559872} a - \frac{2875943}{559872} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2 a + 1\) , \( 2 a + 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a+1\right){x}+2a+37$ |
*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.
