| 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-b1 |
1344.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1344.2 |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{4} \) |
$0.93713$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.127202530$ |
1.228140953 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -14 a - 3\) , \( 35 a - 14\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-14a-3\right){x}+35a-14$ |
| 5376.2-b1 |
5376.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5376.2 |
\( 2^{8} \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{4} \) |
$1.32530$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.127202530$ |
1.228140953 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -14 a - 3\) , \( -35 a + 14\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-14a-3\right){x}-35a+14$ |
| 16128.2-e2 |
16128.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
16128.2 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{4} \) |
$1.74419$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.228140953$ |
1.418135020 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 44 a + 8\) , \( 64 a - 160\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(44a+8\right){x}+64a-160$ |
| 16128.2-g2 |
16128.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
16128.2 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{4} \) |
$1.74419$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.492629364$ |
$1.228140953$ |
2.794459814 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 44 a + 8\) , \( -64 a + 160\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(44a+8\right){x}-64a+160$ |
| 28224.3-d2 |
28224.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.3 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{10} \) |
$2.00611$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.464193648$ |
2.144018622 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -367 a + 89\) , \( -2485 a + 2080\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-367a+89\right){x}-2485a+2080$ |
| 37632.3-d2 |
37632.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{10} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.804006983$ |
0.928387296 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -93 a + 123\) , \( -165 a - 393\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-93a+123\right){x}-165a-393$ |
| 37632.3-j2 |
37632.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{10} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.118949973$ |
$0.804006983$ |
3.934412475 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 123 a - 30\) , \( 165 a + 393\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(123a-30\right){x}+165a+393$ |
| 86016.2-i2 |
86016.2-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86016.2 |
\( 2^{12} \cdot 3 \cdot 7 \) |
\( 2^{28} \cdot 3^{2} \cdot 7^{4} \) |
$2.65060$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.299735277$ |
$1.063601265$ |
3.192516246 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -57 a - 11\) , \( 212 a - 55\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-57a-11\right){x}+212a-55$ |
| 86016.2-bf2 |
86016.2-bf |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86016.2 |
\( 2^{12} \cdot 3 \cdot 7 \) |
\( 2^{28} \cdot 3^{2} \cdot 7^{4} \) |
$2.65060$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.039142408$ |
$1.063601265$ |
5.104853393 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -57 a - 11\) , \( -212 a + 55\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-57a-11\right){x}-212a+55$ |
| 112896.3-q2 |
112896.3-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.3 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{10} \) |
$2.83706$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.099000185$ |
$0.464193648$ |
4.712553729 |
\( \frac{14733184}{7203} a - \frac{30152432}{2401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 280 a - 368\) , \( 2764 a - 2448\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(280a-368\right){x}+2764a-2448$ |
*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.
