| 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 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}+2$ |
| 448.4-a2 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{8} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.891959002$ |
$1.004073929$ |
1.436013054 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \) |
${y}^2={x}^{3}-59{x}-138$ |
| 448.4-a3 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{4} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.945979501$ |
$2.008147859$ |
1.436013054 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \) |
${y}^2={x}^{3}-19{x}+30$ |
| 448.4-a4 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{14} \cdot 7 \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.945979501$ |
$4.016295718$ |
1.436013054 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 7\) , \( 3 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-3a+7\right){x}+3a+4$ |
| 448.4-a5 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{14} \cdot 7 \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.945979501$ |
$4.016295718$ |
1.436013054 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 4\) , \( -3 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(3a+4\right){x}-3a+7$ |
| 448.4-a6 |
448.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.891959002$ |
$1.004073929$ |
1.436013054 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \) |
${y}^2={x}^{3}-299{x}+1990$ |
| 448.4-b1 |
448.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.197869643$ |
1.208681114 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 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 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a - 6\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-6\right){x}-2a-4$ |
| 448.4-b3 |
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 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 10\) , \( 6 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-10\right){x}+6a-16$ |
| 448.4-b4 |
448.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
448.4 |
\( 2^{6} \cdot 7 \) |
\( 2^{22} \cdot 7^{4} \) |
$1.08769$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.598934821$ |
1.208681114 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-40{x}-84$ |
*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.
