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-a5 |
252.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
252.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$0.94197$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.685091833$ |
2.071522989 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
2268.2-a5 |
2268.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2268.2 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{4} \cdot 3^{28} \cdot 7^{8} \) |
$1.63154$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.212924023$ |
$0.228363944$ |
1.528040995 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -936\) , \( -3668\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-936{x}-3668$ |
8064.2-a5 |
8064.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.2 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{22} \cdot 3^{16} \cdot 7^{8} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.242216540$ |
1.464787953 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -520 a - 209\) , \( 2240 a - 399\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-520a-209\right){x}+2240a-399$ |
8064.7-b5 |
8064.7-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.7 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{22} \cdot 3^{16} \cdot 7^{8} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.242216540$ |
1.464787953 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 522 a - 730\) , \( -2448 a + 800\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(522a-730\right){x}-2448a+800$ |
14112.2-c5 |
14112.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.2 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{14} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.129470186$ |
1.565924189 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2185 a + 1457\) , \( -9287 a + 21407\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2185a+1457\right){x}-9287a+21407$ |
14112.5-b5 |
14112.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.5 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{14} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.129470186$ |
1.565924189 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2183 a - 728\) , \( 9286 a + 12120\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2183a-728\right){x}+9286a+12120$ |
16128.5-n5 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{28} \cdot 3^{16} \cdot 7^{8} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1.155405907$ |
$0.171272958$ |
4.786899797 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1664\) , \( -9804\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1664{x}-9804$ |
*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.