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 |
2500.2-a1 |
2500.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{8} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.3 |
$1$ |
\( 3 \) |
$0.214947847$ |
$1.424166746$ |
1.388436963 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}-552$ |
2500.2-a2 |
2500.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{16} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.4 |
$1$ |
\( 3 \) |
$3.224217708$ |
$0.854500048$ |
1.388436963 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-76{x}+298$ |
2500.2-a3 |
2500.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 3 \) |
$0.644843541$ |
$4.272500240$ |
1.388436963 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}-2$ |
2500.2-a4 |
2500.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{30} \cdot 5^{16} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.4 |
$1$ |
\( 3 \) |
$1.074739236$ |
$0.284833349$ |
1.388436963 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+549{x}-2202$ |
2500.2-b1 |
2500.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 5^{20} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 3^{2} \) |
$1.224244896$ |
$0.284833349$ |
4.744742190 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3138{x}-68969$ |
2500.2-b2 |
2500.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{4} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 5^{2} \) |
$0.734546937$ |
$4.272500240$ |
4.744742190 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
2500.2-b3 |
2500.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{20} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 1 \) |
$3.672734688$ |
$0.854500048$ |
4.744742190 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-13{x}-219$ |
2500.2-b4 |
2500.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2500.2 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{30} \cdot 5^{4} \) |
$1.67175$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 3^{2} \cdot 5^{2} \) |
$0.244848979$ |
$1.424166746$ |
4.744742190 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+22{x}-9$ |
*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.