| 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 |
| 868.2-c2 |
868.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.2 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{20} \cdot 7^{3} \cdot 31 \) |
$0.84010$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.989558703$ |
1.148672253 |
\( \frac{10621452329}{10888192} a - \frac{7274546105}{10888192} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -10 a + 8\) , \( 4 a + 12\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-10a+8\right){x}+4a+12$ |
| 54684.2-e1 |
54684.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{20} \cdot 3^{6} \cdot 7^{9} \cdot 31 \) |
$2.36681$ |
$(-2a+1), (-3a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.203114854$ |
$0.434157302$ |
4.073035142 |
\( \frac{10621452329}{10888192} a - \frac{7274546105}{10888192} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -228 a + 108\) , \( 635 a - 1797\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-228a+108\right){x}+635a-1797$ |
| 55552.2-c1 |
55552.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
55552.2 |
\( 2^{8} \cdot 7 \cdot 31 \) |
\( 2^{44} \cdot 7^{3} \cdot 31 \) |
$2.37615$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.497389675$ |
1.723008379 |
\( \frac{10621452329}{10888192} a - \frac{7274546105}{10888192} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 30 a - 163\) , \( -225 a - 930\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(30a-163\right){x}-225a-930$ |
| 146692.2-a1 |
146692.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146692.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{3} \cdot 13^{6} \cdot 31 \) |
$3.02901$ |
$(-3a+1), (-4a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.257585578$ |
$0.551804301$ |
3.282509488 |
\( \frac{10621452329}{10888192} a - \frac{7274546105}{10888192} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 138 a - 44\) , \( 685 a + 155\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(138a-44\right){x}+685a+155$ |
| 146692.6-a1 |
146692.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146692.6 |
\( 2^{2} \cdot 7 \cdot 13^{2} \cdot 31 \) |
\( 2^{20} \cdot 7^{3} \cdot 13^{6} \cdot 31 \) |
$3.02901$ |
$(-3a+1), (4a-3), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.083109647$ |
$0.551804301$ |
3.177292090 |
\( \frac{10621452329}{10888192} a - \frac{7274546105}{10888192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -140 a + 53\) , \( -450 a + 918\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-140a+53\right){x}-450a+918$ |
*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.
