| 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-a6 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$0.94197$ |
$(a+3), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
1.533571636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 13652 a - 38228\) , \( -1309846 a + 3656537\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(13652a-38228\right){x}-1309846a+3656537$ |
| 28.1-b6 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$0.94197$ |
$(a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.436190660$ |
0.856661451 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 252.1-a6 |
252.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \) |
$1.63154$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$5.274317364$ |
$1.010844637$ |
2.326864094 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -8192 a - 16383\) , \( -661749 a - 1158061\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8192a-16383\right){x}-661749a-1158061$ |
| 252.1-d6 |
252.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \) |
$1.63154$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$5.274317364$ |
$1.010844637$ |
2.326864094 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 8191 a - 24575\) , \( 661749 a - 1819810\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8191a-24575\right){x}+661749a-1819810$ |
| 1792.1-d6 |
1792.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1792.1 |
\( 2^{8} \cdot 7 \) |
\( 2^{42} \cdot 7^{4} \) |
$2.66430$ |
$(a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
3.067143272 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -43688\) , \( 3529328\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-43688{x}+3529328$ |
| 1792.1-bp6 |
1792.1-bp |
$6$ |
$18$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1792.1 |
\( 2^{8} \cdot 7 \) |
\( 2^{42} \cdot 7^{4} \) |
$2.66430$ |
$(a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$22.14452561$ |
$0.109047665$ |
4.215635879 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 218442 a - 611635\) , \( 84485431 a - 235853342\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(218442a-611635\right){x}+84485431a-235853342$ |
*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.
