| 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-a7 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.724153859$ |
0.325834452 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 567.1-a7 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{16} \cdot 7^{8} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$5.277017646$ |
$0.574717953$ |
2.292578873 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-441{x}+3672$ |
| 4032.1-c7 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{8} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.609580442$ |
1.843198006 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -245 a - 98\) , \( -2312 a + 816\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-245a-98\right){x}-2312a+816$ |
| 4032.7-c7 |
4032.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.7 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{8} \) |
$1.88394$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.609580442$ |
1.843198006 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 245 a - 343\) , \( 2312 a - 1496\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(245a-343\right){x}+2312a-1496$ |
| 7056.1-c7 |
7056.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{14} \) |
$2.16684$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.325834452$ |
1.970461553 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -1029 a + 686\) , \( 8568 a - 20944\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-1029a+686\right){x}+8568a-20944$ |
| 7056.5-c7 |
7056.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.5 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{14} \) |
$2.16684$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.325834452$ |
1.970461553 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 1029 a - 343\) , \( -8568 a - 12376\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(1029a-343\right){x}-8568a-12376$ |
| 16128.5-i7 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{8} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1.492598417$ |
$0.431038464$ |
3.890719903 |
\( \frac{13027640977}{21609} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -784\) , \( 8704\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-784{x}+8704$ |
| 28224.1-d7 |
28224.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{14} \) |
$3.06438$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.971774980$ |
$0.230399750$ |
2.070326753 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1715 a + 686\) , \( 4760 a - 59024\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1715a+686\right){x}+4760a-59024$ |
| 28224.7-d7 |
28224.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.7 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{14} \) |
$3.06438$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.971774980$ |
$0.230399750$ |
2.070326753 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1715 a + 2400\) , \( -4074 a - 50833\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-1715a+2400\right){x}-4074a-50833$ |
| 36288.1-c7 |
36288.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{8} \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.203193480$ |
1.228798671 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2205 a - 882\) , \( 62424 a - 22032\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2205a-882\right){x}+62424a-22032$ |
| 36288.7-c7 |
36288.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{8} \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.203193480$ |
1.228798671 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2205 a - 3088\) , \( -60219 a + 37304\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2205a-3088\right){x}-60219a+37304$ |
| 39375.1-d7 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{8} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$3.862964642$ |
$0.344830771$ |
8.055596601 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1225\) , \( -17000\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1225{x}-17000$ |
*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.
