| 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 |
| 63.1-a4 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.325834452 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 567.1-a4 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{28} \cdot 7^{2} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.319254411$ |
$0.574717953$ |
2.292578873 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-2430$ |
| 4032.1-c4 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.609580442$ |
1.843198006 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -195 a - 78\) , \( 1530 a - 540\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-195a-78\right){x}+1530a-540$ |
| 4032.7-c4 |
4032.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.7 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{2} \) |
$1.88394$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.609580442$ |
1.843198006 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 195 a - 273\) , \( -1530 a + 990\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(195a-273\right){x}-1530a+990$ |
| 7056.1-c4 |
7056.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 7^{8} \) |
$2.16684$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.325834452$ |
1.970461553 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -819 a + 546\) , \( -5670 a + 13860\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-819a+546\right){x}-5670a+13860$ |
| 7056.5-c4 |
7056.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.5 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 7^{8} \) |
$2.16684$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.325834452$ |
1.970461553 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 819 a - 273\) , \( 5670 a + 8190\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(819a-273\right){x}+5670a+8190$ |
| 16128.5-i5 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{16} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.492598417$ |
$0.431038464$ |
3.890719903 |
\( \frac{6570725617}{45927} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -624\) , \( -5760\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-624{x}-5760$ |
| 28224.1-d5 |
28224.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{8} \) |
$3.06438$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.971774980$ |
$0.230399750$ |
2.070326753 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1365 a + 546\) , \( -3150 a + 39060\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1365a+546\right){x}-3150a+39060$ |
| 28224.7-d5 |
28224.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.7 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{8} \) |
$3.06438$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.971774980$ |
$0.230399750$ |
2.070326753 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1365 a + 1910\) , \( 3696 a + 38641\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-1365a+1910\right){x}+3696a+38641$ |
| 36288.1-c5 |
36288.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{28} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.203193480$ |
1.228798671 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1755 a - 702\) , \( -41310 a + 14580\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1755a-702\right){x}-41310a+14580$ |
| 36288.7-c5 |
36288.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{28} \cdot 7^{2} \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.203193480$ |
1.228798671 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1755 a - 2458\) , \( 43065 a - 29188\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1755a-2458\right){x}+43065a-29188$ |
| 39375.1-d5 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{16} \cdot 5^{12} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.965741160$ |
$0.344830771$ |
8.055596601 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -975\) , \( 11250\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-975{x}+11250$ |
*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.
