| 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-a5 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.370183666$ |
0.791075908 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$ |
| 12348.2-b5 |
12348.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{10} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.298998588$ |
1.381015326 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1260 a + 756\) , \( 17183 a - 33024\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1260a+756\right){x}+17183a-33024$ |
| 12348.3-b5 |
12348.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{10} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.298998588$ |
1.381015326 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -1261 a + 2017\) , \( -17183 a - 15841\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1261a+2017\right){x}-17183a-15841$ |
| 28812.3-f5 |
28812.3-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{16} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.276615502$ |
$0.195740523$ |
4.001350588 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4117 a + 4117\) , \( -101935\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-4117a+4117\right){x}-101935$ |
| 37632.2-r5 |
37632.2-r |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{32} \cdot 3^{8} \cdot 7^{4} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.342545916$ |
3.164303633 |
\( \frac{65597103937}{63504} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1344\) , \( -19404\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1344{x}-19404$ |
| 99372.4-g5 |
99372.4-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.380020574$ |
4.439887655 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -671 a + 1260\) , \( 10579 a + 5784\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-671a+1260\right){x}+10579a+5784$ |
| 99372.6-h5 |
99372.6-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99372.6 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$2.74799$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.316188102$ |
$0.380020574$ |
4.439887655 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1260 a + 673\) , \( -9991 a + 15103\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1260a+673\right){x}-9991a+15103$ |
| 112896.2-k5 |
112896.2-k |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{32} \cdot 3^{14} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.197768977$ |
0.913455777 |
\( \frac{65597103937}{63504} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4033\) , \( -112391 a + 58212\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4033\right){x}-112391a+58212$ |
| 112896.2-u5 |
112896.2-u |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{32} \cdot 3^{14} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.197768977$ |
0.913455777 |
\( \frac{65597103937}{63504} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4032 a\) , \( 116424 a - 58212\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-4032a{x}+116424a-58212$ |
*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.
