| 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 |
| 3872.14-b6 |
3872.14-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 42 a - 62\) , \( -163 a + 81\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(42a-62\right){x}-163a+81$ |
| 3872.5-b6 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -33 a + 71\) , \( -78 a - 204\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-33a+71\right){x}-78a-204$ |
| 5324.6-e6 |
5324.6-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{9} \cdot 11^{9} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.881571669$ |
2.665622171 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -130 a + 152\) , \( -27 a + 1015\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-130a+152\right){x}-27a+1015$ |
| 5324.7-d6 |
5324.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{9} \cdot 11^{9} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.881571669$ |
2.665622171 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 75 a - 202\) , \( 547 a - 934\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(75a-202\right){x}+547a-934$ |
| 15488.20-d5 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{27} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -23 a + 148\) , \( -429 a + 66\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-23a+148\right){x}-429a+66$ |
| 15488.5-d5 |
15488.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{27} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 105 a - 72\) , \( -469 a - 43\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(105a-72\right){x}-469a-43$ |
| 23716.5-a5 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{6} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.527369991$ |
$1.105108572$ |
3.524449760 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -63 a - 58\) , \( 371 a + 62\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-63a-58\right){x}+371a+62$ |
*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.
