| 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-b3 |
3872.14-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{15} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.730960613$ |
2.210217144 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 69 a + 153\) , \( 753 a - 1067\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(69a+153\right){x}+753a-1067$ |
| 3872.5-b3 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{15} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.730960613$ |
2.210217144 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -102 a - 107\) , \( 867 a + 190\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-102a-107\right){x}+867a+190$ |
| 5324.6-e3 |
5324.6-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{3} \cdot 11^{15} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.440785834$ |
2.665622171 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -132 a - 483\) , \( -1724 a - 3749\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-132a-483\right){x}-1724a-3749$ |
| 5324.7-d3 |
5324.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{3} \cdot 11^{15} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.440785834$ |
2.665622171 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 329 a + 211\) , \( -1214 a + 5583\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(329a+211\right){x}-1214a+5583$ |
| 15488.20-d4 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.516867206$ |
1.562859530 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -292 a - 13\) , \( 2282 a - 1707\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-292a-13\right){x}+2282a-1707$ |
| 15488.5-d4 |
15488.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.516867206$ |
1.562859530 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4 a + 422\) , \( 2375 a - 1363\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+422\right){x}+2375a-1363$ |
| 23716.5-a4 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.131842497$ |
$0.552554286$ |
3.524449760 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 231 a - 317\) , \( -2079 a + 1315\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(231a-317\right){x}-2079a+1315$ |
*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.
