| 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 |
| 1008.1-a4 |
1008.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1008.1 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{2} \) |
$1.33215$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.318752128$ |
$2.804887001$ |
1.351697264 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 6 a - 2\) , \( -7 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(6a-2\right){x}-7a+1$ |
| 3528.1-c4 |
3528.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{8} \) |
$1.82209$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.082125192$ |
$1.060147637$ |
3.468844441 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -42 a + 19\) , \( 60 a - 119\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-42a+19\right){x}+60a-119$ |
| 4032.1-b4 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.983354618$ |
1.499275166 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a - 6\) , \( -20 a + 15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-6\right){x}-20a+15$ |
| 8064.5-c4 |
8064.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.5 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.402443500$ |
2.120295274 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 34\) , \( -14 a + 56\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-34\right){x}-14a+56$ |
| 9072.1-b4 |
9072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9072.1 |
\( 2^{4} \cdot 3^{4} \cdot 7 \) |
\( 2^{8} \cdot 3^{20} \cdot 7^{2} \) |
$2.30735$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$0.934962333$ |
2.827060365 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 55 a - 23\) , \( 96 a + 123\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(55a-23\right){x}+96a+123$ |
| 28224.1-f4 |
28224.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{8} \) |
$3.06438$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.749637583$ |
1.133345496 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 61 a + 47\) , \( 108 a - 528\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(61a+47\right){x}+108a-528$ |
| 31752.1-a4 |
31752.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
31752.1 |
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 7^{8} \) |
$3.15595$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.392090523$ |
$0.353382545$ |
2.974976467 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -381 a + 171\) , \( -1837 a + 3982\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-381a+171\right){x}-1837a+3982$ |
| 32256.7-j4 |
32256.7-j |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
32256.7 |
\( 2^{9} \cdot 3^{2} \cdot 7 \) |
\( 2^{26} \cdot 3^{8} \cdot 7^{2} \) |
$3.16840$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.645967249$ |
$0.991677309$ |
4.935515645 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 26 a + 41\) , \( -59 a + 182\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(26a+41\right){x}-59a+182$ |
| 36288.1-b4 |
36288.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{14} \cdot 3^{20} \cdot 7^{2} \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.661118206$ |
0.999516777 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -78 a - 60\) , \( 551 a - 106\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-78a-60\right){x}+551a-106$ |
*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.
