| 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 |
| 5202.6-a1 |
5202.6-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 17^{8} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.369327134$ |
1.044614883 |
\( \frac{3805069}{559872} a - \frac{2875943}{559872} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 3 a + 67\) , \( 1506 a - 1533\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(3a+67\right){x}+1506a-1533$ |
| 5202.6-b1 |
5202.6-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{5} \cdot 3^{32} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
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 |
\( -\frac{811409154866127821}{1647129056757192} a - \frac{79261954805628389}{411782264189298} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 5772 a - 561\) , \( -137153 a - 442749\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5772a-561\right){x}-137153a-442749$ |
| 5202.6-b2 |
5202.6-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.655636803$ |
1.390815689 |
\( \frac{507662}{243} a + \frac{2905757}{486} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -88 a - 86\) , \( -446 a + 48\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-88a-86\right){x}-446a+48$ |
| 5202.6-b3 |
5202.6-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{16} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.327818401$ |
1.390815689 |
\( -\frac{362392621}{118098} a + \frac{474522278}{59049} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -313 a - 466\) , \( 3501 a + 3002\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-313a-466\right){x}+3501a+3002$ |
| 5202.6-b4 |
5202.6-b |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
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 |
\( \frac{105956215006891}{114791256} a + \frac{9859152651013}{459165024} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 6672 a + 959\) , \( -150309 a - 291157\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6672a+959\right){x}-150309a-291157$ |
| 5202.6-c1 |
5202.6-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{5} \cdot 3^{32} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.270325979$ |
1.911493331 |
\( -\frac{811409154866127821}{1647129056757192} a - \frac{79261954805628389}{411782264189298} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 43 a + 476\) , \( 4872 a + 1842\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(43a+476\right){x}+4872a+1842$ |
| 5202.6-c2 |
5202.6-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.703259793$ |
1.911493331 |
\( \frac{507662}{243} a + \frac{2905757}{486} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a - 9\) , \( -9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(3a-9\right){x}-9$ |
| 5202.6-c3 |
5202.6-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{16} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.351629896$ |
1.911493331 |
\( -\frac{362392621}{118098} a + \frac{474522278}{59049} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18 a - 29\) , \( -69 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(18a-29\right){x}-69a+15$ |
| 5202.6-c4 |
5202.6-c |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.540651958$ |
1.911493331 |
\( \frac{105956215006891}{114791256} a + \frac{9859152651013}{459165024} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -17 a + 556\) , \( 3860 a + 290\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-17a+556\right){x}+3860a+290$ |
| 5202.6-d1 |
5202.6-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.6 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{5} \cdot 7 \) |
$0.010099910$ |
$1.522774784$ |
4.872100372 |
\( \frac{3805069}{559872} a - \frac{2875943}{559872} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 1\) , \( -3 a + 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+1\right){x}-3a+37$ |
*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.
