| 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 |
| 147.2-a3 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.497720347 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 3087.2-a3 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{8} \cdot 7^{22} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.188120608$ |
1.737783746 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -816 a + 510\) , \( -13020 a + 24087\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-816a+510\right){x}-13020a+24087$ |
| 3087.3-a3 |
3087.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.3 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{8} \cdot 7^{22} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.188120608$ |
1.737783746 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 816 a - 306\) , \( 13020 a + 11067\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(816a-306\right){x}+13020a+11067$ |
| 7203.3-a3 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{28} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.638508823$ |
$0.123153847$ |
1.500845174 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1667\) , \( 72764\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1667{x}+72764$ |
| 24843.4-b2 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{16} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 510 a - 238\) , \( -7812 a - 3689\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(510a-238\right){x}-7812a-3689$ |
| 24843.6-b2 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{16} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 238 a - 510\) , \( 7812 a - 11501\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(238a-510\right){x}+7812a-11501$ |
| 37632.2-f2 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{16} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.746299208$ |
$0.215519232$ |
2.971586411 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -544\) , \( 13888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-544{x}+13888$ |
| 91875.2-c2 |
91875.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91875.2 |
\( 3 \cdot 5^{4} \cdot 7^{2} \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{16} \) |
$2.69463$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.236287448$ |
$0.172415385$ |
3.010689818 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -850 a + 849\) , \( -26275\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-850a+849\right){x}-26275$ |
| 112896.2-q2 |
112896.2-q |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{16} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.124430086$ |
2.298871812 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1633\) , \( 81695 a - 41664\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1633\right){x}+81695a-41664$ |
| 112896.2-y2 |
112896.2-y |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{16} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.124430086$ |
2.298871812 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1633\) , \( -81695 a + 41664\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1633\right){x}-81695a+41664$ |
*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.
