| 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-a2 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.896615437$ |
0.325834452 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}$ |
| 567.1-a2 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.319254411$ |
$2.298871812$ |
2.292578873 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$ |
| 4032.1-c2 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 5 a + 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(5a+2\right){x}$ |
| 4032.7-c2 |
4032.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.7 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{2} \) |
$1.88394$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -5 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+7\right){x}$ |
| 7056.1-c2 |
7056.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{8} \) |
$2.16684$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.303337809$ |
1.970461553 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 21 a - 14\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(21a-14\right){x}$ |
| 7056.5-c2 |
7056.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.5 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{8} \) |
$2.16684$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.303337809$ |
1.970461553 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -21 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-21a+7\right){x}$ |
| 16128.5-i2 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.373149604$ |
$1.724153859$ |
3.890719903 |
\( \frac{103823}{63} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}$ |
| 28224.1-d2 |
28224.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{8} \) |
$3.06438$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.742943745$ |
$0.921599003$ |
2.070326753 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -35 a - 14\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-35a-14\right){x}$ |
| 28224.7-d2 |
28224.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.7 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{8} \) |
$3.06438$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.742943745$ |
$0.921599003$ |
2.070326753 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 35 a - 50\) , \( -14 a - 69\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(35a-50\right){x}-14a-69$ |
| 36288.1-c2 |
36288.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.812773923$ |
1.228798671 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 45 a + 18\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(45a+18\right){x}$ |
| 36288.7-c2 |
36288.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{2} \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.812773923$ |
1.228798671 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -45 a + 62\) , \( -45 a + 62\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-45a+62\right){x}-45a+62$ |
| 39375.1-d2 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.862964642$ |
$1.379323087$ |
8.055596601 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 25\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+25{x}$ |
*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.
