| 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 |
| 8.1-a3 |
8.1-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.53739$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.974633256$ |
0.573311322 |
\( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( 4 a^{2} + 15 a - 2\) , \( -14 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{2}+15a-2\right){x}-14a^{2}+6a-2$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72566$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.84404198$ |
0.815585101 |
\( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 1\) , \( 54 a^{2} + 61 a - 27\) , \( 214 a^{2} + 250 a - 99\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(54a^{2}+61a-27\right){x}+214a^{2}+250a-99$ |
| 200.2-d3 |
200.2-d |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.62890$ |
$(a^2-a-2), (a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.187272981$ |
$42.04433533$ |
1.941659237 |
\( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) |
\( \bigl[a^{2} - a - 2\) , \( 0\) , \( 0\) , \( 21 a - 21\) , \( 22 a^{2} - 80 a + 39\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(21a-21\right){x}+22a^{2}-80a+39$ |
| 256.1-b3 |
256.1-b |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.73932$ |
$(a^2-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.13621542$ |
1.133042247 |
\( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( 0\) , \( -10 a^{2} + 46 a - 36\) , \( 107 a^{2} - 286 a + 136\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-10a^{2}+46a-36\right){x}+107a^{2}-286a+136$ |
| 256.1-e3 |
256.1-e |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.73932$ |
$(a^2-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$19.37885850$ |
1.592932356 |
\( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( 0\) , \( 30 a^{2} - 10 a - 84\) , \( -110 a^{2} + 78 a + 348\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(30a^{2}-10a-84\right){x}-110a^{2}+78a+348$ |
| 400.2-a3 |
400.2-a |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.95084$ |
$(a^2-a-2), (a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.33048036$ |
1.671155191 |
\( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) |
\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( 42 a^{2} + 21 a - 63\) , \( 57 a^{2} + 130 a + 66\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(42a^{2}+21a-63\right){x}+57a^{2}+130a+66$ |
*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.
