| 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 |
| 12800.7-a1 |
12800.7-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.161293589$ |
$4.117323585$ |
4.016086598 |
\( \frac{10752}{5} a - \frac{83968}{5} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -3 a + 2\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-3a+2\right){x}+a-2$ |
| 12800.7-b1 |
12800.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{25} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.803516140$ |
1.363330055 |
\( \frac{251566}{5} a - \frac{1108938}{5} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a + 40\) , \( -76 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+40\right){x}-76a+4$ |
| 12800.7-b2 |
12800.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{25} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.803516140$ |
1.363330055 |
\( -\frac{251566}{5} a - \frac{857372}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 28 a - 20\) , \( -64 a - 32\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(28a-20\right){x}-64a-32$ |
| 12800.7-b3 |
12800.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{4} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.803516140$ |
1.363330055 |
\( \frac{19652}{25} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a + 5\) , \( -7 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a+5\right){x}-7a-6$ |
| 12800.7-b4 |
12800.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{28} \cdot 5^{8} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.901758070$ |
1.363330055 |
\( \frac{2185454}{625} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -34 a - 35\) , \( -127 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-34a-35\right){x}-127a+2$ |
| 12800.7-c1 |
12800.7-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{14} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 7 \) |
$0.161981579$ |
$0.599237495$ |
4.108976077 |
\( \frac{12459008}{78125} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 31 a + 30\) , \( -367 a - 98\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(31a+30\right){x}-367a-98$ |
| 12800.7-d1 |
12800.7-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.004700957$ |
3.030822964 |
\( -\frac{2249728}{5} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -17 a - 18\) , \( -41 a - 22\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-17a-18\right){x}-41a-22$ |
| 12800.7-e1 |
12800.7-e |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.574683819$ |
$2.548780403$ |
4.428966097 |
\( -\frac{51712}{125} a + \frac{892928}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a + 11\) , \( -8 a + 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a+11\right){x}-8a+3$ |
| 12800.7-f1 |
12800.7-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.312331464$ |
$4.730000215$ |
4.467019669 |
\( \frac{1024}{5} a + \frac{1024}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}+a-1$ |
| 12800.7-g1 |
12800.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{8} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.059560260$ |
3.203809084 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -13 a - 13\) , \( 34 a - 102\bigr] \) |
${y}^2={x}^{3}+\left(-13a-13\right){x}+34a-102$ |
| 12800.7-g2 |
12800.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.119120521$ |
3.203809084 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( 6 a - 18\bigr] \) |
${y}^2={x}^{3}+\left(7a+7\right){x}+6a-18$ |
| 12800.7-g3 |
12800.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.238241043$ |
3.203809084 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( -a + 3\bigr] \) |
${y}^2={x}^{3}+\left(2a+2\right){x}-a+3$ |
| 12800.7-g4 |
12800.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12800.7 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{26} \cdot 5^{2} \) |
$2.51472$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.059560260$ |
3.203809084 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 107 a + 107\) , \( 426 a - 1278\bigr] \) |
${y}^2={x}^{3}+\left(107a+107\right){x}+426a-1278$ |
*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.
