| 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-a1 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.472989750$ |
$4.016295718$ |
1.436013054 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}+2$ |
| 1792.5-c1 |
1792.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1792.5 |
\( 2^{8} \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$1.53823$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.016295718$ |
1.518017094 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}-2$ |
| 3584.4-e1 |
3584.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( 2 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-2\right){x}+2a+4$ |
| 3584.7-e1 |
3584.7-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( -2 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}-2a+6$ |
| 6272.4-a1 |
6272.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.4 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
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-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 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 28 a - 14\bigr] \) |
${y}^2={x}^{3}-7{x}+28a-14$ |
| 7168.5-d1 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a-2\right){x}-2a-4$ |
| 7168.7-d1 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( 2 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}+2a-6$ |
| 25088.4-o2 |
25088.4-o |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.073400181$ |
3.245657071 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7 a + 14\) , \( -70 a + 84\bigr] \) |
${y}^2={x}^{3}+\left(-7a+14\right){x}-70a+84$ |
| 25088.7-o2 |
25088.7-o |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.073400181$ |
3.245657071 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( 70 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(7a+7\right){x}+70a+14$ |
| 28672.7-a2 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.696738583$ |
$2.008147859$ |
4.230644320 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 16\bigr] \) |
${y}^2={x}^{3}+4{x}+16$ |
| 28672.7-m2 |
28672.7-m |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.516662016$ |
$2.008147859$ |
6.274414190 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( -16\bigr] \) |
${y}^2={x}^{3}+4{x}-16$ |
| 36288.4-d2 |
36288.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.4 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{16} \cdot 3^{12} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.294122201$ |
$1.338765239$ |
5.238665667 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( -54\bigr] \) |
${y}^2={x}^{3}+9{x}-54$ |
*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.
