| 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 |
| 567.1-a1 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{16} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$0.287358976$ |
2.292578873 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}+5859$ |
| 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 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$ |
| 567.1-a3 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{20} \cdot 7^{4} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$1.149435906$ |
2.292578873 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}+27$ |
| 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 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-2430$ |
| 567.1-a5 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7 \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.659627205$ |
$2.298871812$ |
2.292578873 |
\( -\frac{2940226}{21} a + \frac{5920433}{21} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 18 a - 3\) , \( 10 a + 36\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(18a-3\right){x}+10a+36$ |
| 567.1-a6 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7 \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.659627205$ |
$2.298871812$ |
2.292578873 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -18 a + 15\) , \( -10 a + 46\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-18a+15\right){x}-10a+46$ |
| 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 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-441{x}+3672$ |
| 567.1-a8 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.55403529$ |
$0.287358976$ |
2.292578873 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
*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.
