| 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 |
| 4.1-b2 |
4.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$32.05257343$ |
6.527611391 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 5894 a - 46359\) , \( -851278 a + 6695693\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(5894a-46359\right){x}-851278a+6695693$ |
| 4.1-c2 |
4.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$14.29159922$ |
2.910530915 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 7682232 a + 52742056\) , \( 18970234890 a + 130239387525\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(7682232a+52742056\right){x}+18970234890a+130239387525$ |
| 36.4-p2 |
36.4-p |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.22436$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$7.134287580$ |
0.484306998 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 18\) , \( 2 a\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+18{x}+2a$ |
| 36.4-t2 |
36.4-t |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.22436$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$21.40286274$ |
1.452920994 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 4507641812667 a + 30947034249657\) , \( 8524947882923374269 a + 58527688106870891311\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4507641812667a+30947034249657\right){x}+8524947882923374269a+58527688106870891311$ |
| 36.5-p2 |
36.5-p |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.22436$ |
$(-a+8), (-a-7), (-52a+409)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$21.40286274$ |
0.484306998 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 3458375228 a - 27201711764\) , \( -382829662027190 a + 3011131367198732\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(3458375228a-27201711764\right){x}-382829662027190a+3011131367198732$ |
| 36.5-t2 |
36.5-t |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.22436$ |
$(-a+8), (-a-7), (-52a+409)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$7.134287580$ |
1.452920994 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 119 a + 827\) , \( -779 a - 5355\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(119a+827\right){x}-779a-5355$ |
*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.
