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 |
2352.2-b1 |
2352.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2352.2 |
\( 2^{4} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \) |
$1.07785$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.872431843$ |
1.511096279 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -113 a + 113\) , \( -516\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-113a+113\right){x}-516$ |
37632.2-a1 |
37632.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.839682332$ |
$0.872431843$ |
2.860688937 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -113\) , \( 516\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-113{x}+516$ |
49392.2-b1 |
49392.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49392.2 |
\( 2^{4} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{18} \) |
$2.30735$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$4.009596522$ |
$0.190380236$ |
3.525753077 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2719 a + 1700\) , \( -29942 a + 54560\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2719a+1700\right){x}-29942a+54560$ |
49392.3-b1 |
49392.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49392.3 |
\( 2^{4} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{18} \) |
$2.30735$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$4.009596522$ |
$0.190380236$ |
3.525753077 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1019 a - 1700\) , \( 29942 a + 24618\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1019a-1700\right){x}+29942a+24618$ |
112896.2-m1 |
112896.2-m |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{12} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.503698759$ |
1.744863686 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 341 a - 340\) , \( -2756 a + 1208\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(341a-340\right){x}-2756a+1208$ |
112896.2-w1 |
112896.2-w |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{12} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.503698759$ |
1.744863686 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -339 a\) , \( 3096 a - 1548\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-339a{x}+3096a-1548$ |
115248.3-b1 |
115248.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
115248.3 |
\( 2^{4} \cdot 3 \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{24} \) |
$2.85172$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.997905620$ |
$0.124633120$ |
3.450317426 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5553\) , \( 165894\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5553{x}+165894$ |
*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.