| 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 |
| 588.2-a2 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.342545916$ |
0.791075908 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
| 12348.2-b2 |
12348.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{38} \cdot 7^{10} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.074749647$ |
1.381015326 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -5790 a - 3474\) , \( 69683 a - 123240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5790a-3474\right){x}+69683a-123240$ |
| 12348.3-b2 |
12348.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{38} \cdot 7^{10} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.074749647$ |
1.381015326 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 5789 a - 9263\) , \( -69683 a - 53557\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(5789a-9263\right){x}-69683a-53557$ |
| 28812.3-f2 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{16} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.106462011$ |
$0.048935130$ |
4.001350588 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 18913 a - 18913\) , \( -381333\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(18913a-18913\right){x}-381333$ |
| 37632.2-r2 |
37632.2-r |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{32} \cdot 7^{4} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$1$ |
$0.085636479$ |
3.164303633 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 6176\) , \( -69388\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+6176{x}-69388$ |
| 99372.4-g2 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.095005143$ |
4.439887655 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 3089 a - 5790\) , \( 40575 a + 15536\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3089a-5790\right){x}+40575a+15536$ |
| 99372.6-h2 |
99372.6-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.6 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.095005143$ |
4.439887655 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 5790 a - 3087\) , \( -43277 a + 61901\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5790a-3087\right){x}-43277a+61901$ |
| 112896.2-k2 |
112896.2-k |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{38} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.049442244$ |
0.913455777 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 18527\) , \( -434855 a + 208164\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-18527\right){x}-434855a+208164$ |
| 112896.2-u2 |
112896.2-u |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 3^{38} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.049442244$ |
0.913455777 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18528 a\) , \( 416328 a - 208164\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+18528a{x}+416328a-208164$ |
*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.
