| 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 |
| 48400.8-a1 |
48400.8-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{16} \cdot 5^{12} \cdot 11^{2} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$2.121504889$ |
$0.718716509$ |
6.915663990 |
\( \frac{436334416}{171875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -100\) , \( -252\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-100{x}-252$ |
| 48400.8-a2 |
48400.8-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 11^{4} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.530376222$ |
$1.437433019$ |
6.915663990 |
\( \frac{643956736}{15125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -45\) , \( 100\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-45{x}+100$ |
| 48400.8-a3 |
48400.8-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 11^{12} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$4.773386000$ |
$0.479144339$ |
6.915663990 |
\( \frac{610462990336}{8857805} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -445\) , \( -3720\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-445{x}-3720$ |
| 48400.8-a4 |
48400.8-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{16} \cdot 5^{4} \cdot 11^{6} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$19.09354400$ |
$0.239572169$ |
6.915663990 |
\( \frac{154639330142416}{33275} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7100\) , \( -232652\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7100{x}-232652$ |
| 48400.8-b1 |
48400.8-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 11^{4} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.978126157$ |
2.251251767 |
\( \frac{1048576}{605} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5{x}+2$ |
| 48400.8-b2 |
48400.8-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{16} \cdot 5^{4} \cdot 11^{2} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.489063078$ |
2.251251767 |
\( \frac{94875856}{275} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -60\) , \( 200\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-60{x}+200$ |
| 48400.8-c1 |
48400.8-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 5^{4} \cdot 11^{7} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.451828368$ |
$0.849914256$ |
5.225190037 |
\( -\frac{746020960272}{44289025} a - \frac{79785457056}{44289025} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -55 a + 118\) , \( 185 a + 331\bigr] \) |
${y}^2={x}^{3}+\left(-55a+118\right){x}+185a+331$ |
| 48400.8-c2 |
48400.8-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 5^{8} \cdot 11^{5} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.225914184$ |
$0.849914256$ |
5.225190037 |
\( \frac{1066404528}{831875} a + \frac{188347248}{831875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -49 a + 31\) , \( -25 a + 212\bigr] \) |
${y}^2={x}^{3}+\left(-49a+31\right){x}-25a+212$ |
| 48400.8-d1 |
48400.8-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 5^{4} \cdot 11^{7} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.451828368$ |
$0.849914256$ |
5.225190037 |
\( \frac{746020960272}{44289025} a - \frac{825806417328}{44289025} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 55 a + 63\) , \( -185 a + 516\bigr] \) |
${y}^2={x}^{3}+\left(55a+63\right){x}-185a+516$ |
| 48400.8-d2 |
48400.8-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
48400.8 |
\( 2^{4} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 5^{8} \cdot 11^{5} \) |
$3.50670$ |
$(a), (-a+1), (-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.225914184$ |
$0.849914256$ |
5.225190037 |
\( -\frac{1066404528}{831875} a + \frac{1254751776}{831875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 49 a - 18\) , \( 25 a + 187\bigr] \) |
${y}^2={x}^{3}+\left(49a-18\right){x}+25a+187$ |
*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.
