| 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 |
| 1764.2-a2 |
1764.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1764.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$1.92070$ |
$(-a), (a-1), (2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.115234789$ |
$0.342545916$ |
1.747716634 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
| 882.1-a2 |
882.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
882.1 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{32} \cdot 7^{4} \) |
$4.56822$ |
$(2,a), (3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$2.115234789$ |
$0.342545916$ |
4.943289135 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 1569\) , \( 5581\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+1569{x}+5581$ |
| 84.2-c2 |
84.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-231}) \) |
$2$ |
$[0, 1]$ |
84.2 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \cdot 11^{12} \) |
$4.11163$ |
$(2,a), (2,a+1), (3,a+1), (7,a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$9.361707760$ |
$0.342545916$ |
3.375886736 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 46704\) , \( -1466406\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+46704{x}-1466406$ |
| 588.1-j2 |
588.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
588.1 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$2.52778$ |
$(-a-2), (-a+3), (-2a+7), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$2.115234789$ |
$0.621721819$ |
1.831418963 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 142040 a + 336962\) , \( -19036524 a - 45159990\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(142040a+336962\right){x}-19036524a-45159990$ |
| 252.1-e2 |
252.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$3.12417$ |
$(a+3), (2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.115234789$ |
$0.621721819$ |
4.795780588 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3478 a + 13524\) , \( -74762 a - 290645\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3478a+13524\right){x}-74762a-290645$ |
*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.
