| 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 |
| 1344.2-b2 |
1344.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1344.2 |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{8} \cdot 7 \) |
$0.93713$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.127202530$ |
1.228140953 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a + 2\) , \( -3 a - 15\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a+2\right){x}-3a-15$ |
| 5376.2-b2 |
5376.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5376.2 |
\( 2^{8} \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{8} \cdot 7 \) |
$1.32530$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.127202530$ |
1.228140953 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 11 a + 2\) , \( 3 a + 15\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(11a+2\right){x}+3a+15$ |
| 16128.2-e3 |
16128.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
16128.2 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{14} \cdot 7 \) |
$1.74419$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.228140953$ |
1.418135020 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -31 a - 7\) , \( -131 a + 56\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-7\right){x}-131a+56$ |
| 16128.2-g3 |
16128.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
16128.2 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{14} \cdot 7 \) |
$1.74419$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.492629364$ |
$1.228140953$ |
2.794459814 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a - 7\) , \( 131 a - 56\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a-7\right){x}+131a-56$ |
| 28224.3-d3 |
28224.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.3 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 7^{7} \) |
$2.00611$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.464193648$ |
2.144018622 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 278 a - 61\) , \( 803 a + 1141\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(278a-61\right){x}+803a+1141$ |
| 37632.3-d3 |
37632.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{7} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.804006983$ |
0.928387296 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 72 a - 92\) , \( -360 a + 360\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(72a-92\right){x}-360a+360$ |
| 37632.3-j3 |
37632.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{7} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.529737493$ |
$0.804006983$ |
3.934412475 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 20\) , \( 360 a - 360\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-92a+20\right){x}+360a-360$ |
| 86016.2-i3 |
86016.2-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86016.2 |
\( 2^{12} \cdot 3 \cdot 7 \) |
\( 2^{28} \cdot 3^{8} \cdot 7 \) |
$2.65060$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.299735277$ |
$1.063601265$ |
3.192516246 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43 a + 9\) , \( 28 a - 163\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43a+9\right){x}+28a-163$ |
| 86016.2-bf3 |
86016.2-bf |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86016.2 |
\( 2^{12} \cdot 3 \cdot 7 \) |
\( 2^{28} \cdot 3^{8} \cdot 7 \) |
$2.65060$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.259785602$ |
$1.063601265$ |
5.104853393 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a + 9\) , \( -28 a + 163\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a+9\right){x}-28a+163$ |
| 112896.3-q3 |
112896.3-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.3 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 7^{7} \) |
$2.83706$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.099000185$ |
$0.464193648$ |
4.712553729 |
\( \frac{2145056}{567} a - \frac{583312}{189} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -215 a + 277\) , \( -1019 a - 864\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-215a+277\right){x}-1019a-864$ |
*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.
