| 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 |
| 132496.3-CMj1 |
132496.3-CMj |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 7^{10} \cdot 13^{6} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$0.305432078$ |
1.058047757 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 5370 a - 2183\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+5370a-2183$ |
| 132496.3-CMi1 |
132496.3-CMi |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 7^{6} \cdot 13^{8} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.381027892$ |
5.279677357 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 1318 a - 2781\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+1318a-2781$ |
| 132496.3-CMh1 |
132496.3-CMh |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 7^{6} \cdot 13^{2} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.056670366$ |
$1.373815605$ |
4.315141795 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -14 a - 43\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-14a-43$ |
| 132496.3-CMg1 |
132496.3-CMg |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 7^{2} \cdot 13^{10} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$0.475334011$ |
1.646605316 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -914 a - 499\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-914a-499$ |
| 132496.3-CMf1 |
132496.3-CMf |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 7^{2} \cdot 13^{4} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 3 \) |
$1$ |
$1.713841151$ |
5.936919900 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -30 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-30a+11$ |
| 132496.3-CMe1 |
132496.3-CMe |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 7^{10} \cdot 13^{10} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$0.206199145$ |
0.714294792 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 1211 a - 15772\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+1211a-15772$ |
| 132496.3-CMd1 |
132496.3-CMd |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 7^{10} \cdot 13^{4} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 3 \) |
$1$ |
$0.743461591$ |
2.575426499 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -229 a - 142\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-229a-142$ |
| 132496.3-CMc1 |
132496.3-CMc |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 7^{6} \cdot 13^{6} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.927471681$ |
3.212856150 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -186 a + 138\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-186a+138$ |
| 132496.3-CMc2 |
132496.3-CMc |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 7^{6} \cdot 13^{6} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.463735840$ |
3.212856150 |
\( 54000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 401 a - 495\) , \( -4189 a + 3332\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(401a-495\right){x}-4189a+3332$ |
| 132496.3-CMb1 |
132496.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 7^{2} \cdot 13^{8} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 3 \) |
$0.349613053$ |
$1.157025097$ |
5.605069911 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -11 a + 91\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-11a+91$ |
| 132496.3-CMa1 |
132496.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
132496.3 |
\( 2^{4} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 7^{2} \cdot 13^{2} \) |
$2.95291$ |
$(-3a+1), (4a-3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.099785968$ |
$4.171713316$ |
5.768123455 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+a+1$ |
*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.
