| 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 |
| 1936.1-a1 |
1936.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1936.1 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{6} \) |
$2.71628$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1.332676418$ |
$0.647455648$ |
3.389203095 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-77{x}-289$ |
| 1936.1-a2 |
1936.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1936.1 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{2} \) |
$2.71628$ |
$(2), (11)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$3.998029254$ |
$5.827100832$ |
3.389203095 |
\( \frac{8192}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+3{x}-1$ |
| 1936.1-b1 |
1936.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1936.1 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{6} \) |
$2.71628$ |
$(2), (11)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1.303707704$ |
$9.327341860$ |
5.307114712 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 387 a - 1081\) , \( -6550 a + 18283\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(387a-1081\right){x}-6550a+18283$ |
| 1936.1-b2 |
1936.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1936.1 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{2} \) |
$2.71628$ |
$(2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.434569234$ |
$9.327341860$ |
5.307114712 |
\( \frac{8192}{11} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 39\) , \( -38 a + 107\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-13a+39\right){x}-38a+107$ |
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*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.
