| 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 |
| 10.2-a1 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$35.64539671$ |
0.808454015 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 166 a - 413\) , \( -1827 a + 4480\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(166a-413\right){x}-1827a+4480$ |
| 10.2-b1 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.683258437$ |
1.255225901 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -117 a - 292\) , \( -1111 a - 2738\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-117a-292\right){x}-1111a-2738$ |
| 80.1-a1 |
80.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{13} \cdot 5 \) |
$1.30923$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$0.341629218$ |
1.255225901 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -466 a - 1175\) , \( -8421 a - 20735\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-466a-1175\right){x}-8421a-20735$ |
| 80.1-b1 |
80.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{13} \cdot 5 \) |
$1.30923$ |
$(-a+2), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.053388319$ |
$17.82269835$ |
1.553832031 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 664 a - 1650\) , \( -14616 a + 35842\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(664a-1650\right){x}-14616a+35842$ |
| 450.2-b1 |
450.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.765090763$ |
$1.570369906$ |
1.962001293 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -320 a - 1302\) , \( 8071 a + 15740\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-320a-1302\right){x}+8071a+15740$ |
| 450.2-l1 |
450.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$1.033939752$ |
3.798937226 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 10427 a - 25568\) , \( -900947 a + 2206823\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10427a-25568\right){x}-900947a+2206823$ |
*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.
