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-a4 |
252.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
252.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$0.94197$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.342545916$ |
2.071522989 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
2268.2-a4 |
2268.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2268.2 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{2} \cdot 3^{44} \cdot 7^{4} \) |
$1.63154$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.425848046$ |
$0.114181972$ |
1.528040995 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3474\) , \( -31010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3474{x}-31010$ |
8064.2-a4 |
8064.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.2 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{32} \cdot 7^{4} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.121108270$ |
1.464787953 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1930 a + 771\) , \( 19782 a - 8435\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1930a+771\right){x}+19782a-8435$ |
8064.7-b4 |
8064.7-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.7 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{32} \cdot 7^{4} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.121108270$ |
1.464787953 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1928 a + 2700\) , \( -19010 a + 15206\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1928a+2700\right){x}-19010a+15206$ |
14112.2-c4 |
14112.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.2 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{32} \cdot 7^{10} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.064735093$ |
1.565924189 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 8105 a - 5403\) , \( -69655 a + 175071\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8105a-5403\right){x}-69655a+175071$ |
14112.5-b4 |
14112.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14112.5 |
\( 2^{5} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{32} \cdot 7^{10} \) |
$2.57682$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.064735093$ |
1.565924189 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -8107 a + 2702\) , \( 69654 a + 105416\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-8107a+2702\right){x}+69654a+105416$ |
16128.5-n4 |
16128.5-n |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{26} \cdot 3^{32} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$2.310811814$ |
$0.085636479$ |
4.786899797 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 6176\) , \( -69388\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+6176{x}-69388$ |
*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.