| 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-a7 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.497720347 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 3087.2-a7 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{10} \cdot 7^{14} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.376241217$ |
1.737783746 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -1176 a + 735\) , \( -8160 a + 15096\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-1176a+735\right){x}-8160a+15096$ |
| 3087.3-a7 |
3087.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.3 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{10} \cdot 7^{14} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.376241217$ |
1.737783746 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1176 a - 441\) , \( 8160 a + 6936\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1176a-441\right){x}+8160a+6936$ |
| 7203.3-a7 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{4} \cdot 7^{20} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.319254411$ |
$0.246307694$ |
1.500845174 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2402\) , \( 44246\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2402{x}+44246$ |
| 24843.4-b7 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{8} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 735 a - 343\) , \( -4896 a - 2312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(735a-343\right){x}-4896a-2312$ |
| 24843.6-b7 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{8} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 343 a - 735\) , \( 4896 a - 7208\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(343a-735\right){x}+4896a-7208$ |
| 37632.2-f7 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 7^{8} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.492598417$ |
$0.431038464$ |
2.971586411 |
\( \frac{13027640977}{21609} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -784\) , \( 8704\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-784{x}+8704$ |
| 91875.2-c7 |
91875.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91875.2 |
\( 3 \cdot 5^{4} \cdot 7^{2} \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{8} \) |
$2.69463$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.472574897$ |
$0.344830771$ |
3.010689818 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1225 a + 1224\) , \( -15775\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1225a+1224\right){x}-15775$ |
| 112896.2-q7 |
112896.2-q |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 7^{8} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.248860173$ |
2.298871812 |
\( \frac{13027640977}{21609} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2353\) , \( 49871 a - 26112\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2353\right){x}+49871a-26112$ |
| 112896.2-y7 |
112896.2-y |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 7^{8} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.248860173$ |
2.298871812 |
\( \frac{13027640977}{21609} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2353\) , \( -49871 a + 26112\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2353\right){x}-49871a+26112$ |
*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.
