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 |
252.2-a2 |
252.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
252.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{2} \cdot 7 \) |
$0.94197$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$2.740367332$ |
2.071522989 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 2 a - 11\) , \( -6 a + 11\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a-11\right){x}-6a+11$ |
2268.2-a2 |
2268.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2268.2 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{20} \cdot 3^{14} \cdot 7 \) |
$1.63154$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.276615502$ |
$0.913455777$ |
1.528040995 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 18 a - 93\) , \( 80 a - 323\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(18a-93\right){x}+80a-323$ |
8064.2-a2 |
8064.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.2 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{38} \cdot 3^{2} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.968866161$ |
1.464787953 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -38 a - 40\) , \( 196 a + 56\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-38a-40\right){x}+196a+56$ |
8064.7-b2 |
8064.7-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.7 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{38} \cdot 3^{2} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.968866161$ |
1.464787953 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 55 a - 54\) , \( -203 a - 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(55a-54\right){x}-203a-26$ |
14112.2-c1 |
14112.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.2 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{32} \cdot 3^{2} \cdot 7^{7} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.517880747$ |
1.565924189 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -204 a + 62\) , \( -1071 a + 1605\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-204a+62\right){x}-1071a+1605$ |
14112.5-b1 |
14112.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.5 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{32} \cdot 3^{2} \cdot 7^{7} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.517880747$ |
1.565924189 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 189 a + 10\) , \( 364 a + 1336\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(189a+10\right){x}+364a+1336$ |
16128.5-n1 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{44} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.310811814$ |
$0.685091833$ |
4.786899797 |
\( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 33 a - 166\) , \( 234 a - 744\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-166\right){x}+234a-744$ |
*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.