| 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 |
| 2.1-a2 |
2.1-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.71558$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$1.618379814$ |
1.613958003 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( -82 a^{2} + 19 a + 473\) , \( -18 a^{2} + 123 a - 195\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-82a^{2}+19a+473\right){x}-18a^{2}+123a-195$ |
| 16.3-a2 |
16.3-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{15} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$3.085948894$ |
2.051678216 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[0\) , \( a + 1\) , \( a^{2} - 4\) , \( -938 a^{2} - 1396 a + 3056\) , \( -29345 a^{2} - 44566 a + 93184\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-938a^{2}-1396a+3056\right){x}-29345a^{2}-44566a+93184$ |
| 50.2-a2 |
50.2-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( - 2^{3} \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 3 \) |
$1$ |
$2.992575047$ |
2.984398597 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( a + 1\) , \( -44 a^{2} - 7 a + 246\) , \( -83 a^{2} - 111 a + 467\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-44a^{2}-7a+246\right){x}-83a^{2}-111a+467$ |
| 64.4-a1 |
64.4-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{21} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$32.89239640$ |
2.429816763 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - 4\) , \( -899 a^{2} + 3309 a - 2633\) , \( 46108 a^{2} - 170423 a + 136781\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-899a^{2}+3309a-2633\right){x}+46108a^{2}-170423a+136781$ |
| 64.4-n2 |
64.4-n |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{21} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.067701501$ |
$8.624963052$ |
4.081655584 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[0\) , \( -a^{2} + 6\) , \( a^{2} - 4\) , \( -165 a^{2} + 224 a + 480\) , \( -1313 a^{2} + 3235 a + 180\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-165a^{2}+224a+480\right){x}-1313a^{2}+3235a+180$ |
| 98.2-a2 |
98.2-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( - 2^{3} \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$2.332758095$ |
0.775461475 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( -57 a^{2} + 29 a + 268\) , \( 38 a^{2} - 326 a + 486\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-57a^{2}+29a+268\right){x}+38a^{2}-326a+486$ |
*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.
