| 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 |
| 44.1-a1 |
44.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{6} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.058354610$ |
$4.914891725$ |
0.401901529 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -77\) , \( 289\bigr] \) |
${y}^2={x}^3-{x}^2-77{x}+289$ |
| 44.1-b1 |
44.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \cdot 13^{12} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$2.323199861$ |
$4.914891725$ |
5.333469382 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 78 a + 3058\) , \( 3977 a - 29040\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(78a+3058\right){x}+3977a-29040$ |
| 44.1-c1 |
44.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \cdot 29^{12} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$7.556040036$ |
$4.914891725$ |
11.56448306 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 1006 a - 9934\) , \( -58343 a + 213508\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(1006a-9934\right){x}-58343a+213508$ |
| 44.1-d1 |
44.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \cdot 19^{12} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$4.914891725$ |
4.591485623 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 542 a - 654\) , \( -13895 a - 107718\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(542a-654\right){x}-13895a-107718$ |
| 44.1-e1 |
44.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{6} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$4.914891725$ |
1.530495207 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \) |
${y}^2={x}^3+{x}^2-77{x}-289$ |
| 44.1-f1 |
44.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \cdot 13^{12} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$2.767124560$ |
$4.914891725$ |
12.70521263 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 78 a + 3058\) , \( -3978 a + 29122\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(78a+3058\right){x}-3978a+29122$ |
| 44.1-g1 |
44.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \cdot 29^{12} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$14.33062577$ |
$4.914891725$ |
10.96647703 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 1006 a - 9934\) , \( 58342 a - 213426\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(1006a-9934\right){x}+58342a-213426$ |
| 44.1-h1 |
44.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \cdot 19^{12} \) |
$5.91253$ |
$(2,a+1), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$9$ |
\( 2 \cdot 3 \) |
$0.546704862$ |
$4.914891725$ |
11.29584381 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 542 a - 654\) , \( 13894 a + 107800\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(542a-654\right){x}+13894a+107800$ |
*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.
