| 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 |
| 1024.1-a1 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$0.87554$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.992347595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 1024.1-a2 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$0.87554$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.437592909$ |
0.992347595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
| 4096.1-c1 |
4096.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$1.23820$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.444312937$ |
$6.875185818$ |
1.763651500 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}$ |
| 4096.1-c2 |
4096.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{24} \) |
$1.23820$ |
$(2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.888625874$ |
$3.437592909$ |
1.763651500 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+4\right){x}$ |
| 9216.1-d1 |
9216.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.501182392$ |
$3.969390382$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(3a-3\right){x}$ |
| 9216.1-d2 |
9216.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$1.51647$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.250591196$ |
$1.984695191$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-12a+12\right){x}$ |
| 36864.1-j1 |
36864.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$0.571185187$ |
$5.224011530$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}$ |
| 36864.1-j2 |
36864.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{3} \) |
$0.285592593$ |
$2.612005765$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-4\right){x}$ |
| 36864.1-k1 |
36864.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.508042231$ |
1.741337176 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(24a-12\right){x}$ |
| 36864.1-k2 |
36864.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$1$ |
$3.016084463$ |
1.741337176 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a+3\right){x}$ |
| 36864.1-n1 |
36864.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{3} \) |
$0.285592593$ |
$2.612005765$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-8\right){x}$ |
| 36864.1-n2 |
36864.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$0.571185187$ |
$5.224011530$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+2\right){x}$ |
| 36864.1-o1 |
36864.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$1$ |
$3.016084463$ |
1.741337176 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a-3\right){x}$ |
| 36864.1-o2 |
36864.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.508042231$ |
1.741337176 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a + 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-24a+12\right){x}$ |
| 36864.1-p1 |
36864.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.984695191$ |
2.291728606 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(12a-12\right){x}$ |
| 36864.1-p2 |
36864.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.969390382$ |
2.291728606 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-3a+3\right){x}$ |
| 50176.1-i1 |
50176.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.31645$ |
$(-3a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.598575984$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-5a-3\right){x}$ |
| 50176.1-i2 |
50176.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.31645$ |
$(-3a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.299287992$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 20 a + 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(20a+12\right){x}$ |
| 50176.3-g1 |
50176.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50176.3 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.31645$ |
$(3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.598575984$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(5a-8\right){x}$ |
| 50176.3-g2 |
50176.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50176.3 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.31645$ |
$(3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.299287992$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -20 a + 32\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-20a+32\right){x}$ |
| 65536.1-c1 |
65536.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
65536.1 |
\( 2^{16} \) |
\( 2^{18} \) |
$2.47639$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.608709031$ |
$4.861490513$ |
3.417028151 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2{x}$ |
| 65536.1-c2 |
65536.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
65536.1 |
\( 2^{16} \) |
\( 2^{30} \) |
$2.47639$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.217418063$ |
$2.430745256$ |
3.417028151 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+8{x}$ |
| 65536.1-d1 |
65536.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
65536.1 |
\( 2^{16} \) |
\( 2^{30} \) |
$2.47639$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.429482697$ |
$2.430745256$ |
4.012247529 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+8a{x}$ |
| 65536.1-d2 |
65536.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
65536.1 |
\( 2^{16} \) |
\( 2^{18} \) |
$2.47639$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.714741348$ |
$4.861490513$ |
4.012247529 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2a{x}$ |
*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.
