| 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-a8 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.497720347 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 3087.2-a8 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{8} \cdot 7^{10} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.188120608$ |
1.737783746 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -18816 a + 11760\) , \( -510900 a + 945165\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-18816a+11760\right){x}-510900a+945165$ |
| 3087.3-a8 |
3087.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.3 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{8} \cdot 7^{10} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.188120608$ |
1.737783746 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 18816 a - 7056\) , \( 510900 a + 434265\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(18816a-7056\right){x}+510900a+434265$ |
| 7203.3-a8 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{16} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$0.123153847$ |
1.500845174 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -38417\) , \( 2882228\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-38417{x}+2882228$ |
| 24843.4-b8 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 11760 a - 5488\) , \( -306540 a - 144755\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(11760a-5488\right){x}-306540a-144755$ |
| 24843.6-b8 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 5488 a - 11760\) , \( 306540 a - 451295\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5488a-11760\right){x}+306540a-451295$ |
| 37632.2-f8 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{4} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.985196834$ |
$0.215519232$ |
2.971586411 |
\( \frac{53297461115137}{147} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12544\) , \( 544960\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-12544{x}+544960$ |
| 91875.2-c8 |
91875.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91875.2 |
\( 3 \cdot 5^{4} \cdot 7^{2} \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{4} \) |
$2.69463$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.945149794$ |
$0.172415385$ |
3.010689818 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -19600 a + 19599\) , \( -1044775\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-19600a+19599\right){x}-1044775$ |
| 112896.2-q8 |
112896.2-q |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.124430086$ |
2.298871812 |
\( \frac{53297461115137}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 37633\) , \( 3232127 a - 1634880\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+37633\right){x}+3232127a-1634880$ |
| 112896.2-y8 |
112896.2-y |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.124430086$ |
2.298871812 |
\( \frac{53297461115137}{147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 37633\) , \( -3232127 a + 1634880\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+37633\right){x}-3232127a+1634880$ |
*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.
