| 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 |
| 6272.5-a1 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.518017094$ |
1.147513062 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 28 a - 14\bigr] \) |
${y}^2={x}^{3}-7{x}+28a-14$ |
| 6272.5-a2 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{14} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.379504273$ |
1.147513062 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 413\) , \( -1932 a + 966\bigr] \) |
${y}^2={x}^{3}+413{x}-1932a+966$ |
| 6272.5-a3 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.759008547$ |
1.147513062 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 133\) , \( 420 a - 210\bigr] \) |
${y}^2={x}^{3}+133{x}+420a-210$ |
| 6272.5-a4 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.518017094$ |
1.147513062 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 49\) , \( 77 a - 112\bigr] \) |
${y}^2={x}^{3}+\left(21a-49\right){x}+77a-112$ |
| 6272.5-a5 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.518017094$ |
1.147513062 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21 a - 28\) , \( 77 a + 35\bigr] \) |
${y}^2={x}^{3}+\left(-21a-28\right){x}+77a+35$ |
| 6272.5-a6 |
6272.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.379504273$ |
1.147513062 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2093\) , \( 27860 a - 13930\bigr] \) |
${y}^2={x}^{3}+2093{x}+27860a-13930$ |
| 6272.5-b1 |
6272.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.182292284$ |
$5.622082628$ |
3.098892262 |
\( 12544 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+1$ |
| 6272.5-c1 |
6272.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.928648180$ |
1.403984080 |
\( -1474 a + 1114 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 19 a + 39\) , \( 104 a - 100\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(19a+39\right){x}+104a-100$ |
| 6272.5-c2 |
6272.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.928648180$ |
1.403984080 |
\( 1474 a - 360 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -19 a + 58\) , \( 104 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+58\right){x}+104a-4$ |
| 6272.5-d1 |
6272.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.891191201$ |
$1.208681114$ |
3.257043758 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -58 a + 28\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-58a+28$ |
| 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 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 28 a + 40\) , \( -84 a + 216\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(28a+40\right){x}-84a+216$ |
| 6272.5-d3 |
6272.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.445595600$ |
$1.208681114$ |
3.257043758 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -28 a + 68\) , \( -84 a - 132\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-28a+68\right){x}-84a-132$ |
| 6272.5-d4 |
6272.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.782382402$ |
$0.604340557$ |
3.257043758 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 282\) , \( -1458 a + 588\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+282\right){x}-1458a+588$ |
| 6272.5-e1 |
6272.5-e |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2 \cdot 3 \) |
$0.145911714$ |
$2.367335951$ |
3.133374295 |
\( -512 a + 256 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a + 2\) , \( 8 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a+2\right){x}+8a-3$ |
| 6272.5-f1 |
6272.5-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.5 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$1.399015357$ |
2.115112409 |
\( 48384 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 49\) , \( 98 a - 49\bigr] \) |
${y}^2={x}^{3}+49{x}+98a-49$ |
*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.
