| 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-a6 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.497720347 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 3087.2-a6 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{22} \cdot 7^{8} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.376241217$ |
1.737783746 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -936 a + 585\) , \( 5400 a - 9990\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-936a+585\right){x}+5400a-9990$ |
| 3087.3-a6 |
3087.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.3 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{22} \cdot 7^{8} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.376241217$ |
1.737783746 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 936 a - 351\) , \( -5400 a - 4590\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(936a-351\right){x}-5400a-4590$ |
| 7203.3-a6 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{16} \cdot 7^{14} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.319254411$ |
$0.246307694$ |
1.500845174 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1912\) , \( -32782\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1912{x}-32782$ |
| 24843.4-b6 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 7^{2} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 585 a - 273\) , \( 3240 a + 1530\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(585a-273\right){x}+3240a+1530$ |
| 24843.6-b6 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 7^{2} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 273 a - 585\) , \( -3240 a + 4770\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(273a-585\right){x}-3240a+4770$ |
| 37632.2-f6 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{16} \cdot 7^{2} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.492598417$ |
$0.431038464$ |
2.971586411 |
\( \frac{6570725617}{45927} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -624\) , \( -5760\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-624{x}-5760$ |
| 91875.2-c6 |
91875.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91875.2 |
\( 3 \cdot 5^{4} \cdot 7^{2} \) |
\( 3^{16} \cdot 5^{12} \cdot 7^{2} \) |
$2.69463$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.890299589$ |
$0.344830771$ |
3.010689818 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -975 a + 974\) , \( 12225\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-975a+974\right){x}+12225$ |
| 112896.2-q6 |
112896.2-q |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{22} \cdot 7^{2} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.248860173$ |
2.298871812 |
\( \frac{6570725617}{45927} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1873\) , \( -36433 a + 17280\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1873\right){x}-36433a+17280$ |
| 112896.2-y6 |
112896.2-y |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{22} \cdot 7^{2} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.248860173$ |
2.298871812 |
\( \frac{6570725617}{45927} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1873\) , \( 36433 a - 17280\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1873\right){x}+36433a-17280$ |
*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.
