| 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 |
| 28.1-a4 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$0.94197$ |
$(a+3), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
1.533571636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 177 a - 498\) , \( -1497 a + 4175\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(177a-498\right){x}-1497a+4175$ |
| 28.1-b4 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$0.94197$ |
$(a+3), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.856661451 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 252.1-a4 |
252.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{12} \) |
$1.63154$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1.758105788$ |
$3.032533911$ |
2.326864094 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -107 a - 213\) , \( -837 a - 1465\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-107a-213\right){x}-837a-1465$ |
| 252.1-d4 |
252.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{12} \) |
$1.63154$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1.758105788$ |
$3.032533911$ |
2.326864094 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 106 a - 320\) , \( 837 a - 2302\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(106a-320\right){x}+837a-2302$ |
| 1792.1-d4 |
1792.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1792.1 |
\( 2^{8} \cdot 7 \) |
\( 2^{30} \cdot 7^{12} \) |
$2.66430$ |
$(a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
3.067143272 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -568\) , \( 4464\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-568{x}+4464$ |
| 1792.1-bp4 |
1792.1-bp |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1792.1 |
\( 2^{8} \cdot 7 \) |
\( 2^{30} \cdot 7^{12} \) |
$2.66430$ |
$(a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$2.460502846$ |
$0.981428986$ |
4.215635879 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2842 a - 7955\) , \( 104295 a - 291134\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2842a-7955\right){x}+104295a-291134$ |
*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.
