| 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 |
| 50700.3-a1 |
50700.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{11} \cdot 5^{4} \cdot 13^{8} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.301248308$ |
0.695703166 |
\( \frac{46880677}{291600} a + \frac{205902887}{583200} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 386 a - 127\) , \( -4431 a + 3411\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(386a-127\right){x}-4431a+3411$ |
| 50700.3-b1 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.643233601$ |
$0.358971497$ |
2.724511424 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -203 a + 108\) , \( 2295 a - 3379\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-203a+108\right){x}+2295a-3379$ |
| 50700.3-b2 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.547744533$ |
$1.076914492$ |
2.724511424 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 22 a - 12\) , \( -81 a + 119\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(22a-12\right){x}-81a+119$ |
| 50700.3-b3 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$6.572934406$ |
$0.089742874$ |
2.724511424 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -6803 a + 3628\) , \( 19575 a - 28819\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6803a+3628\right){x}+19575a-28819$ |
| 50700.3-b4 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.190978135$ |
$0.269228623$ |
2.724511424 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -1028 a + 548\) , \( 6975 a - 10269\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-1028a+548\right){x}+6975a-10269$ |
| 50700.3-b5 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.095489067$ |
$0.538457246$ |
2.724511424 |
\( \frac{702595369}{72900} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -278 a + 148\) , \( -945 a + 1391\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-278a+148\right){x}-945a+1391$ |
| 50700.3-b6 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.286467203$ |
$0.179485748$ |
2.724511424 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -5003 a + 2668\) , \( 85239 a - 125491\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5003a+2668\right){x}+85239a-125491$ |
| 50700.3-b7 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.190978135$ |
$0.269228623$ |
2.724511424 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -4328 a + 2308\) , \( -67041 a + 98699\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4328a+2308\right){x}-67041a+98699$ |
| 50700.3-b8 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$6.572934406$ |
$0.089742874$ |
2.724511424 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -80003 a + 42668\) , \( 5413239 a - 7969491\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-80003a+42668\right){x}+5413239a-7969491$ |
| 50700.3-c1 |
50700.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{11} \cdot 5^{4} \cdot 13^{2} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 11 \) |
$0.015980506$ |
$1.086166221$ |
4.409393735 |
\( \frac{46880677}{291600} a + \frac{205902887}{583200} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -22 a - 7\) , \( -51 a + 99\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-22a-7\right){x}-51a+99$ |
*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.
