| 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 |
| 448.4-b2 |
448.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.197869643$ |
1.208681114 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a - 6\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-6\right){x}-2a-4$ |
| 1792.5-a2 |
1792.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1792.5 |
\( 2^{8} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$1.53823$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.479839797$ |
$3.197869643$ |
2.319893204 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a - 6\) , \( 2 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-6\right){x}+2a+4$ |
| 3584.4-b2 |
3584.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.261235310$ |
1.709333224 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 19\) , \( -29 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+19\right){x}-29a+11$ |
| 3584.7-b2 |
3584.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.261235310$ |
1.709333224 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 3\) , \( -13 a - 14\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(14a-3\right){x}-13a-14$ |
| 6272.4-d2 |
6272.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.4 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.445595600$ |
$1.208681114$ |
3.257043758 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 28 a + 40\) , \( 84 a - 216\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(28a+40\right){x}+84a-216$ |
| 6272.5-d2 |
6272.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.782382402$ |
$1.208681114$ |
3.257043758 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 28 a + 40\) , \( -84 a + 216\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(28a+40\right){x}-84a+216$ |
| 7168.5-g2 |
7168.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.075549531$ |
$2.261235310$ |
3.676945099 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 19\) , \( 29 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+19\right){x}+29a-11$ |
| 7168.7-g2 |
7168.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.268887382$ |
$2.261235310$ |
3.676945099 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a - 3\) , \( 13 a + 14\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(14a-3\right){x}+13a+14$ |
| 25088.4-j3 |
25088.4-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{7} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.953158940$ |
$0.854666612$ |
4.926438062 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 12 a - 136\) , \( 36 a - 600\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(12a-136\right){x}+36a-600$ |
| 25088.7-j3 |
25088.7-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{7} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.953158940$ |
$0.854666612$ |
4.926438062 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -96 a + 16\) , \( -384 a + 480\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-96a+16\right){x}-384a+480$ |
| 28672.7-d3 |
28672.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.422246907$ |
$1.598934821$ |
4.082894903 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -15 a - 23\) , \( 69 a + 25\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-23\right){x}+69a+25$ |
| 28672.7-p3 |
28672.7-p |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.598934821$ |
2.417362229 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 23\) , \( -69 a - 25\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-23\right){x}-69a-25$ |
| 36288.4-f3 |
36288.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{19} \cdot 3^{12} \cdot 7 \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.065956547$ |
1.611574819 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -36 a - 51\) , \( 172 a + 94\bigr] \) |
${y}^2={x}^{3}+\left(-36a-51\right){x}+172a+94$ |
*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.
