| 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-a5 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.448307718$ |
0.497720347 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 3087.2-a5 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{14} \cdot 7^{10} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.752482435$ |
1.737783746 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -96 a + 60\) , \( -60 a + 111\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-96a+60\right){x}-60a+111$ |
| 3087.3-a5 |
3087.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.3 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{14} \cdot 7^{10} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.752482435$ |
1.737783746 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 96 a - 36\) , \( 60 a + 51\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(96a-36\right){x}+60a+51$ |
| 7203.3-a5 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{8} \cdot 7^{16} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.659627205$ |
$0.492615388$ |
1.500845174 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -197\) , \( 146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-197{x}+146$ |
| 24843.4-b4 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.956388484$ |
2.208684594 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 60 a - 28\) , \( -36 a - 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(60a-28\right){x}-36a-17$ |
| 24843.6-b4 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.956388484$ |
2.208684594 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 28 a - 60\) , \( 36 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(28a-60\right){x}+36a-53$ |
| 37632.2-f4 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{4} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.746299208$ |
$0.862076929$ |
2.971586411 |
\( \frac{7189057}{3969} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+64$ |
| 91875.2-c4 |
91875.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91875.2 |
\( 3 \cdot 5^{4} \cdot 7^{2} \) |
\( 3^{8} \cdot 5^{12} \cdot 7^{4} \) |
$2.69463$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.945149794$ |
$0.689661543$ |
3.010689818 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -100 a + 99\) , \( -25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-100a+99\right){x}-25$ |
| 112896.2-q4 |
112896.2-q |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.497720347$ |
2.298871812 |
\( \frac{7189057}{3969} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 193\) , \( 191 a - 192\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+193\right){x}+191a-192$ |
| 112896.2-y4 |
112896.2-y |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.497720347$ |
2.298871812 |
\( \frac{7189057}{3969} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 193\) , \( -191 a + 192\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+193\right){x}-191a+192$ |
*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.
