| 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 |
| 252.1-a1 |
252.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{4} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.724148694$ |
$15.45742511$ |
2.991581821 |
\( -\frac{16384}{147} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 160 a - 594\) , \( -8458 a + 31645\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(160a-594\right){x}-8458a+31645$ |
| 252.1-a2 |
252.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.362074347$ |
$30.91485022$ |
2.991581821 |
\( \frac{20720464}{63} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -12\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-12{x}-2$ |
| 252.1-b1 |
252.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$8.943509084$ |
$0.533054337$ |
3.822404740 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -113\) , \( -516\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-113{x}-516$ |
| 252.1-b2 |
252.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.981169694$ |
$4.797489038$ |
3.822404740 |
\( \frac{2048000}{1323} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+7{x}$ |
| 252.1-b3 |
252.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.490584847$ |
$9.594978077$ |
3.822404740 |
\( \frac{9826000}{5103} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -853 a - 3169\) , \( -8575 a - 32064\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-853a-3169\right){x}-8575a-32064$ |
| 252.1-b4 |
252.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{6} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$4.471754542$ |
$1.066108675$ |
3.822404740 |
\( \frac{2640279346000}{3087} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 54853 a - 205219\) , \( 13539589 a - 50660484\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(54853a-205219\right){x}+13539589a-50660484$ |
| 252.1-c1 |
252.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$3.501042828$ |
$5.711517702$ |
5.344227444 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -13600 a - 50882\) , \( 1736782 a + 6498445\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-13600a-50882\right){x}+1736782a+6498445$ |
| 252.1-c2 |
252.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.389004758$ |
$5.711517702$ |
5.344227444 |
\( \frac{2048000}{1323} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -800 a + 2998\) , \( -7126 a + 26665\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-800a+2998\right){x}-7126a+26665$ |
| 252.1-c3 |
252.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.097251189$ |
$11.42303540$ |
5.344227444 |
\( \frac{9826000}{5103} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -5\) , \( -3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-5{x}-3$ |
| 252.1-c4 |
252.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{6} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.875260707$ |
$11.42303540$ |
5.344227444 |
\( \frac{2640279346000}{3087} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -455\) , \( 3381\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-455{x}+3381$ |
| 252.1-d1 |
252.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{4} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$3.782729173$ |
4.043907586 |
\( -\frac{16384}{147} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}-2$ |
| 252.1-d2 |
252.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
252.1 |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$2.66430$ |
$(-a+4), (-2a+7), (3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$7.565458346$ |
4.043907586 |
\( \frac{20720464}{63} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1087 a - 4067\) , \( -40783 a - 152596\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1087a-4067\right){x}-40783a-152596$ |
*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.
