| 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 |
| 50700.1-a1 |
50700.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{11} \cdot 5^{4} \cdot 13^{8} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.301248308$ |
0.695703166 |
\( -\frac{46880677}{291600} a + \frac{299664241}{583200} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 259 a + 127\) , \( 4431 a - 1020\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(259a+127\right){x}+4431a-1020$ |
| 50700.1-b1 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.643233601$ |
$0.358971497$ |
2.724511424 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 202 a - 95\) , \( -2295 a - 1084\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(202a-95\right){x}-2295a-1084$ |
| 50700.1-b2 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.547744533$ |
$1.076914492$ |
2.724511424 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -23 a + 10\) , \( 81 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23a+10\right){x}+81a+38$ |
| 50700.1-b3 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$6.572934406$ |
$0.089742874$ |
2.724511424 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 6802 a - 3175\) , \( -19575 a - 9244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(6802a-3175\right){x}-19575a-9244$ |
| 50700.1-b4 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.190978135$ |
$0.269228623$ |
2.724511424 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 1027 a - 480\) , \( -6975 a - 3294\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(1027a-480\right){x}-6975a-3294$ |
| 50700.1-b5 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.095489067$ |
$0.538457246$ |
2.724511424 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 277 a - 130\) , \( 945 a + 446\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(277a-130\right){x}+945a+446$ |
| 50700.1-b6 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.286467203$ |
$0.179485748$ |
2.724511424 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5002 a - 2335\) , \( -85239 a - 40252\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(5002a-2335\right){x}-85239a-40252$ |
| 50700.1-b7 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.190978135$ |
$0.269228623$ |
2.724511424 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 4327 a - 2020\) , \( 67041 a + 31658\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(4327a-2020\right){x}+67041a+31658$ |
| 50700.1-b8 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$6.572934406$ |
$0.089742874$ |
2.724511424 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 80002 a - 37335\) , \( -5413239 a - 2556252\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(80002a-37335\right){x}-5413239a-2556252$ |
| 50700.1-c1 |
50700.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{11} \cdot 5^{4} \cdot 13^{2} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 11 \) |
$0.015980506$ |
$1.086166221$ |
4.409393735 |
\( -\frac{46880677}{291600} a + \frac{299664241}{583200} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 7 a + 22\) , \( 51 a + 48\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(7a+22\right){x}+51a+48$ |
*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.
