| 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 |
| 49.1-CMa1 |
49.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$0.40949$ |
$(-3a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$10.15449534$ |
0.239293902 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 49.3-CMa1 |
49.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 7^{2} \) |
$0.40949$ |
$(3a-2)$ |
0 |
$\Z/7\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$10.15449534$ |
0.239293902 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a$ |
| 81.1-CMa1 |
81.1-CMa |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$0.46432$ |
$(-2a+1)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$8.108628264$ |
0.346779163 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 144.1-CMa1 |
144.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$0.53615$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.108115717$ |
0.491528664 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) |
${y}^2={x}^{3}+1$ |
| 256.1-CMb1 |
256.1-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$0.61910$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$8.847515954$ |
0.638514464 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
| 256.1-CMa1 |
256.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$0.61910$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$8.847515954$ |
0.638514464 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 441.1-CMa1 |
441.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$0.70927$ |
$(-2a+1), (-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1[2], 7Cs.6.1 |
$1$ |
\( 3 \) |
$1$ |
$2.215892550$ |
0.852897440 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -10 a + 14\bigr] \) |
${y}^2+a{y}={x}^{3}-10a+14$ |
| 441.3-CMa1 |
441.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
441.3 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$0.70927$ |
$(-2a+1), (3a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1[2], 7Cs.6.1 |
$1$ |
\( 3 \) |
$1$ |
$2.215892550$ |
0.852897440 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 9 a + 4\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+9a+4$ |
| 729.1-CMb1 |
729.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$0.80423$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$8.108628264$ |
1.040337491 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a$ |
| 729.1-CMa1 |
729.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$0.80423$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$8.108628264$ |
1.040337491 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}$ |
| 784.1-CMb1 |
784.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{10} \) |
$0.81899$ |
$(-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$1.101251020$ |
1.271615146 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 94 a - 105\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+94a-105$ |
| 784.1-CMa1 |
784.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{6} \) |
$0.81899$ |
$(-3a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2, 7$ |
2Cs, 7Cs.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.344046705$ |
0.965343132 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -2 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-2a+4$ |
| 784.3-CMb1 |
784.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{10} \) |
$0.81899$ |
$(3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$1.101251020$ |
1.271615146 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -94 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-94a-11$ |
| 784.3-CMa1 |
784.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{6} \) |
$0.81899$ |
$(3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2, 7$ |
2Cs, 7Cs.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.344046705$ |
0.965343132 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 2 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+2a+2$ |
| 961.1-CMa1 |
961.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
961.1 |
\( 31^{2} \) |
\( 31^{10} \) |
$0.86175$ |
$(-6a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$31$ |
31Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$0.802983472$ |
0.927205448 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( 287 a - 76\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}+287a-76$ |
| 961.3-CMa1 |
961.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
961.3 |
\( 31^{2} \) |
\( 31^{10} \) |
$0.86175$ |
$(6a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$31$ |
31Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$0.802983472$ |
0.927205448 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( -287 a + 211\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-287a+211$ |
| 1296.1-CMa1 |
1296.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{6} \) |
$0.92865$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.217911259$ |
1.238574621 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 4\bigr] \) |
${y}^2={x}^{3}+4$ |
| 1521.1-CMb1 |
1521.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{10} \) |
$0.96657$ |
$(-2a+1), (-4a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$13$ |
13Cs.5.1 |
$1$ |
\( 1 \) |
$1$ |
$0.956447781$ |
1.104410767 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -136 a + 165\bigr] \) |
${y}^2+a{y}={x}^{3}-136a+165$ |
| 1521.1-CMa1 |
1521.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{4} \) |
$0.96657$ |
$(-2a+1), (-4a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 13$ |
3B.1.1[2], 13Cs.5.1 |
$1$ |
\( 3 \) |
$1$ |
$3.448521516$ |
1.327336550 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -4 a + 2\bigr] \) |
${y}^2+a{y}={x}^{3}-4a+2$ |
| 1521.3-CMb1 |
1521.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{10} \) |
$0.96657$ |
$(-2a+1), (4a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$13$ |
13Cs.5.1 |
$1$ |
\( 1 \) |
$1$ |
$0.956447781$ |
1.104410767 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 135 a + 29\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+135a+29$ |
| 1521.3-CMa1 |
1521.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1521.3 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 13^{4} \) |
$0.96657$ |
$(-2a+1), (4a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 13$ |
3B.1.1[2], 13Cs.5.1 |
$1$ |
\( 3 \) |
$1$ |
$3.448521516$ |
1.327336550 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 3 a - 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+3a-2$ |
| 1849.1-CMa1 |
1849.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1849.1 |
\( 43^{2} \) |
\( 43^{2} \) |
$1.01492$ |
$(-7a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.4.1 |
$1$ |
\( 1 \) |
$0.022264396$ |
$7.503489439$ |
0.771620158 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
| 1849.3-CMa1 |
1849.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1849.3 |
\( 43^{2} \) |
\( 43^{2} \) |
$1.01492$ |
$(7a-6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.4.1 |
$1$ |
\( 1 \) |
$0.022264396$ |
$7.503489439$ |
0.771620158 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 2304.1-CMa1 |
2304.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$5.108115717$ |
1.474585992 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
| 2401.3-CMd1 |
2401.3-CMd |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2401.3 |
\( 7^{4} \) |
\( 7^{14} \) |
$1.08342$ |
$(-3a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.450642192$ |
1.675057320 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( -27 a + 50\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-27a+50$ |
| 2401.3-CMc1 |
2401.3-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2401.3 |
\( 7^{4} \) |
\( 7^{14} \) |
$1.08342$ |
$(-3a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.4 |
$1$ |
\( 1 \) |
$1$ |
$1.450642192$ |
1.675057320 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( -10 a + 48\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-10a+48$ |
| 2401.3-CMb1 |
2401.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2401.3 |
\( 7^{4} \) |
\( 7^{14} \) |
$1.08342$ |
$(-3a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.4 |
$1$ |
\( 1 \) |
$1$ |
$1.450642192$ |
1.675057320 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a\) , \( 9 a + 38\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}+9a+38$ |
| 2401.3-CMa1 |
2401.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2401.3 |
\( 7^{4} \) |
\( 7^{14} \) |
$1.08342$ |
$(-3a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.450642192$ |
1.675057320 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( 27 a + 23\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+27a+23$ |
| 3969.1-CMc1 |
3969.1-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{10} \) |
$1.22848$ |
$(-2a+1), (-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$0.924992894$ |
1.068089793 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -159 a + 177\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-159a+177$ |
| 3969.1-CMb1 |
3969.1-CMb |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.22848$ |
$(-2a+1), (-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Cs[2], 7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$1.769447752$ |
2.043182272 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 15 a - 28\bigr] \) |
${y}^2+{y}={x}^{3}+15a-28$ |
| 3969.1-CMa1 |
3969.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{4} \) |
$1.22848$ |
$(-2a+1), (-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$4.238849958$ |
1.631534109 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-2$ |
| 3969.3-CMc1 |
3969.3-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.3 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{10} \) |
$1.22848$ |
$(-2a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$0.924992894$ |
1.068089793 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 158 a + 19\bigr] \) |
${y}^2+a{y}={x}^{3}+158a+19$ |
| 3969.3-CMb1 |
3969.3-CMb |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.3 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.22848$ |
$(-2a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Cs[2], 7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$1.769447752$ |
2.043182272 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -15 a - 13\bigr] \) |
${y}^2+{y}={x}^{3}-15a-13$ |
| 3969.3-CMa1 |
3969.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3969.3 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{4} \) |
$1.22848$ |
$(-2a+1), (3a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$4.238849958$ |
1.631534109 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -a - 1\bigr] \) |
${y}^2+a{y}={x}^{3}-a-1$ |
| 4096.1-CMb1 |
4096.1-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{20} \) |
$1.23820$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.423757977$ |
1.277028929 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+2a-1$ |
| 4096.1-CMa1 |
4096.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{20} \) |
$1.23820$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.423757977$ |
1.277028929 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-2a+1$ |
| 4489.1-CMa1 |
4489.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4489.1 |
\( 67^{2} \) |
\( 67^{10} \) |
$1.26688$ |
$(9a-7)$ |
$0 \le r \le 2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$67$ |
67Cs.9.1 |
$4$ |
\( 1 \) |
$1$ |
$0.422453600$ |
1.951229600 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a\) , \( 2040 a - 987\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+2040a-987$ |
| 4489.3-CMa1 |
4489.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4489.3 |
\( 67^{2} \) |
\( 67^{10} \) |
$1.26688$ |
$(9a-2)$ |
$0 \le r \le 2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$67$ |
67Cs.9.1 |
$4$ |
\( 1 \) |
$1$ |
$0.422453600$ |
1.951229600 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a\) , \( -2041 a + 1054\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-2041a+1054$ |
| 5625.1-CMb1 |
5625.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5625.1 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{16} \) |
$1.34039$ |
$(-2a+1), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.1[2], 5Cn.0.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.948390915$ |
1.460143333 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 156\bigr] \) |
${y}^2+{y}={x}^{3}+156$ |
| 5625.1-CMa1 |
5625.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5625.1 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.34039$ |
$(-2a+1), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Cn.0.1 |
$1$ |
\( 2^{2} \) |
$0.017703945$ |
$4.741954575$ |
1.551017859 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}+1$ |
| 5776.1-CMc1 |
5776.1-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.1 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{10} \) |
$1.34929$ |
$(-5a+3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 3 \) |
$1$ |
$0.760664859$ |
2.635020368 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -349 a + 190\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-349a+190$ |
| 5776.1-CMb1 |
5776.1-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.1 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{6} \) |
$1.34929$ |
$(-5a+3), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2, 19$ |
2Cs, 19Cs.4.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.029759365$ |
1.757823174 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -6 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-6a-12$ |
| 5776.1-CMa1 |
5776.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.1 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{2} \) |
$1.34929$ |
$(-5a+3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 3 \) |
$0.018683933$ |
$5.416213237$ |
1.402215272 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+a-1$ |
| 5776.3-CMc1 |
5776.3-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.3 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{10} \) |
$1.34929$ |
$(-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 3 \) |
$1$ |
$0.760664859$ |
2.635020368 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 349 a - 159\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+349a-159$ |
| 5776.3-CMb1 |
5776.3-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.3 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{6} \) |
$1.34929$ |
$(-5a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2, 19$ |
2Cs, 19Cs.4.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.029759365$ |
1.757823174 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 6 a - 18\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+6a-18$ |
| 5776.3-CMa1 |
5776.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.3 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{2} \) |
$1.34929$ |
$(-5a+2), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 3 \) |
$0.018683933$ |
$5.416213237$ |
1.402215272 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a$ |
| 6241.1-CMa1 |
6241.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6241.1 |
\( 79^{2} \) |
\( 79^{2} \) |
$1.37567$ |
$(10a-7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$79$ |
79Cs.8.1 |
$1$ |
\( 1 \) |
$0.043046721$ |
$6.780111505$ |
1.348050840 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-a$ |
| 6241.3-CMa1 |
6241.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6241.3 |
\( 79^{2} \) |
\( 79^{2} \) |
$1.37567$ |
$(10a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$79$ |
79Cs.8.1 |
$1$ |
\( 1 \) |
$0.043046721$ |
$6.780111505$ |
1.348050840 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
| 6561.1-CMf1 |
6561.1-CMf |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6561.1 |
\( 3^{8} \) |
\( 3^{14} \) |
$1.39297$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.898221876$ |
1.500426299 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -3 a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-3a$ |
| 6561.1-CMe1 |
6561.1-CMe |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6561.1 |
\( 3^{8} \) |
\( 3^{14} \) |
$1.39297$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.898221876$ |
1.500426299 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 2 a - 2\bigr] \) |
${y}^2+a{y}={x}^{3}+2a-2$ |
*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.
