| 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 |
| 12544.2-a1 |
12544.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.239919898$ |
$3.197869643$ |
1.771847702 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+4$ |
| 12544.2-a2 |
12544.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.119959949$ |
$1.598934821$ |
1.771847702 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -40\) , \( 84\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-40{x}+84$ |
| 12544.2-b1 |
12544.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.065389884$ |
$1.050244234$ |
1.903187096 |
\( \frac{70330790}{117649} a - \frac{91085936}{117649} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -24 a + 36\) , \( 92 a + 48\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-24a+36\right){x}+92a+48$ |
| 12544.2-b2 |
12544.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.130779768$ |
$2.100488469$ |
1.903187096 |
\( -\frac{2555300}{343} a + \frac{1035204}{343} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a - 4\) , \( 12 a + 16\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(16a-4\right){x}+12a+16$ |
| 12544.2-c1 |
12544.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.130779768$ |
$2.100488469$ |
1.903187096 |
\( \frac{2555300}{343} a - \frac{1520096}{343} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a + 4\) , \( -12 a + 28\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a+4\right){x}-12a+28$ |
| 12544.2-c2 |
12544.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.065389884$ |
$1.050244234$ |
1.903187096 |
\( -\frac{70330790}{117649} a - \frac{20755146}{117649} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 36\) , \( -92 a + 140\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a-36\right){x}-92a+140$ |
| 12544.2-d1 |
12544.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.229781889$ |
1.287365174 |
\( \frac{12853728}{2401} a - \frac{20030544}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 7\) , \( 16 a - 22\bigr] \) |
${y}^2={x}^{3}+\left(-15a+7\right){x}+16a-22$ |
| 12544.2-d2 |
12544.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.229781889$ |
1.287365174 |
\( -\frac{12853728}{2401} a - \frac{7176816}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 8\) , \( 16 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(15a-8\right){x}+16a+6$ |
| 12544.2-d3 |
12544.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.459563779$ |
1.287365174 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}+2{x}+2a-1$ |
| 12544.2-d4 |
12544.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.229781889$ |
1.287365174 |
\( \frac{21882096}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 37\) , \( 100 a - 50\bigr] \) |
${y}^2={x}^{3}+37{x}+100a-50$ |
| 12544.2-e1 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{7} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$2.528755315$ |
$0.423720304$ |
2.474488549 |
\( \frac{308817493407}{2401} a - \frac{61895989485}{2401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 88 a - 1624\) , \( -2480 a + 24592\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(88a-1624\right){x}-2480a+24592$ |
| 12544.2-e2 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{13} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.842918438$ |
$0.423720304$ |
2.474488549 |
\( \frac{2097781165791}{13841287201} a - \frac{295085536866}{13841287201} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a + 63\) , \( -359 a - 1441\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(74a+63\right){x}-359a-1441$ |
| 12544.2-e3 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{13} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$2.528755315$ |
$0.423720304$ |
2.474488549 |
\( -\frac{2097781165791}{13841287201} a + \frac{1802695628925}{13841287201} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -72 a + 136\) , \( -432 a + 1936\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-72a+136\right){x}-432a+1936$ |
| 12544.2-e4 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.210729609$ |
$1.694881218$ |
2.474488549 |
\( \frac{988929}{343} a + \frac{1141344}{343} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 17\) , \( 9 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-17\right){x}+9a+15$ |
| 12544.2-e5 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{4} \) |
$1.264377657$ |
$0.847440609$ |
2.474488549 |
\( \frac{854150427}{117649} a + \frac{702560952}{117649} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 104\) , \( -48 a + 336\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-104\right){x}-48a+336$ |
| 12544.2-e6 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.632188828$ |
$1.694881218$ |
2.474488549 |
\( -\frac{988929}{343} a + \frac{2130273}{343} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 24\) , \( 16 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-24\right){x}+16a-48$ |
| 12544.2-e7 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.421459219$ |
$0.847440609$ |
2.474488549 |
\( -\frac{854150427}{117649} a + \frac{1556711379}{117649} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 97\) , \( -55 a - 385\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-97\right){x}-55a-385$ |
| 12544.2-e8 |
12544.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{7} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.842918438$ |
$0.423720304$ |
2.474488549 |
\( -\frac{308817493407}{2401} a + \frac{246921503922}{2401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 1537\) , \( -2567 a - 23649\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-86a-1537\right){x}-2567a-23649$ |
| 12544.2-f1 |
12544.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.446077502$ |
1.669786470 |
\( \frac{334159992}{2401} a - \frac{339280596}{2401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 41 a - 63\) , \( -161 a + 196\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(41a-63\right){x}-161a+196$ |
| 12544.2-f2 |
12544.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.446077502$ |
1.669786470 |
\( -\frac{334159992}{2401} a - \frac{5120604}{2401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -39 a - 23\) , \( -121 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39a-23\right){x}-121a-12$ |
| 12544.2-f3 |
12544.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.892155004$ |
1.669786470 |
\( \frac{11664}{49} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 3\) , \( -5 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-3\right){x}-5a+4$ |
| 12544.2-f4 |
12544.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.784310009$ |
1.669786470 |
\( \frac{55296}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -2 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-2a$ |
| 12544.2-g1 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{7} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.842918438$ |
$0.423720304$ |
2.474488549 |
\( \frac{308817493407}{2401} a - \frac{61895989485}{2401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1623 a + 1537\) , \( 2567 a - 26216\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1623a+1537\right){x}+2567a-26216$ |
| 12544.2-g2 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{13} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$2.528755315$ |
$0.423720304$ |
2.474488549 |
\( \frac{2097781165791}{13841287201} a - \frac{295085536866}{13841287201} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 74 a + 63\) , \( 359 a + 1441\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(74a+63\right){x}+359a+1441$ |
| 12544.2-g3 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{13} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.842918438$ |
$0.423720304$ |
2.474488549 |
\( -\frac{2097781165791}{13841287201} a + \frac{1802695628925}{13841287201} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 137 a - 63\) , \( 359 a - 1800\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(137a-63\right){x}+359a-1800$ |
| 12544.2-g4 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.632188828$ |
$1.694881218$ |
2.474488549 |
\( \frac{988929}{343} a + \frac{1141344}{343} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 17\) , \( -9 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-17\right){x}-9a-15$ |
| 12544.2-g5 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.421459219$ |
$0.847440609$ |
2.474488549 |
\( \frac{854150427}{117649} a + \frac{702560952}{117649} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -103 a + 97\) , \( 55 a - 440\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-103a+97\right){x}+55a-440$ |
| 12544.2-g6 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.210729609$ |
$1.694881218$ |
2.474488549 |
\( -\frac{988929}{343} a + \frac{2130273}{343} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a + 17\) , \( -9 a + 24\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a+17\right){x}-9a+24$ |
| 12544.2-g7 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{4} \) |
$1.264377657$ |
$0.847440609$ |
2.474488549 |
\( -\frac{854150427}{117649} a + \frac{1556711379}{117649} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 97\) , \( 55 a + 385\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-97\right){x}+55a+385$ |
| 12544.2-g8 |
12544.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{7} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$2.528755315$ |
$0.423720304$ |
2.474488549 |
\( -\frac{308817493407}{2401} a + \frac{246921503922}{2401} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -86 a - 1537\) , \( 2567 a + 23649\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-86a-1537\right){x}+2567a+23649$ |
| 12544.2-h1 |
12544.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.229781889$ |
1.287365174 |
\( \frac{12853728}{2401} a - \frac{20030544}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 7\) , \( -16 a + 22\bigr] \) |
${y}^2={x}^{3}+\left(-15a+7\right){x}-16a+22$ |
| 12544.2-h2 |
12544.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.229781889$ |
1.287365174 |
\( -\frac{12853728}{2401} a - \frac{7176816}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 8\) , \( -16 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(15a-8\right){x}-16a-6$ |
| 12544.2-h3 |
12544.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.459563779$ |
1.287365174 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}+2{x}-2a+1$ |
| 12544.2-h4 |
12544.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.229781889$ |
1.287365174 |
\( \frac{21882096}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 37\) , \( -100 a + 50\bigr] \) |
${y}^2={x}^{3}+37{x}-100a+50$ |
| 12544.2-i1 |
12544.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.446077502$ |
1.669786470 |
\( \frac{334159992}{2401} a - \frac{339280596}{2401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -62 a + 23\) , \( 121 a - 133\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-62a+23\right){x}+121a-133$ |
| 12544.2-i2 |
12544.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{5} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.446077502$ |
1.669786470 |
\( -\frac{334159992}{2401} a - \frac{5120604}{2401} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a + 63\) , \( 161 a + 35\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a+63\right){x}+161a+35$ |
| 12544.2-i3 |
12544.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.892155004$ |
1.669786470 |
\( \frac{11664}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 3\) , \( 5 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+3\right){x}+5a-1$ |
| 12544.2-i4 |
12544.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.784310009$ |
1.669786470 |
\( \frac{55296}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 2\) , \( 2 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-2\right){x}+2a-2$ |
| 12544.2-j1 |
12544.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.284457192$ |
$4.016295718$ |
2.638408062 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}-2$ |
| 12544.2-j2 |
12544.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.284457192$ |
$1.004073929$ |
2.638408062 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( 138\bigr] \) |
${y}^2={x}^{3}-59{x}+138$ |
| 12544.2-j3 |
12544.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.568914384$ |
$2.008147859$ |
2.638408062 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( -30\bigr] \) |
${y}^2={x}^{3}-19{x}-30$ |
| 12544.2-j4 |
12544.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.137828769$ |
$1.004073929$ |
2.638408062 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( -1990\bigr] \) |
${y}^2={x}^{3}-299{x}-1990$ |
| 12544.2-k1 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{60} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$6.314005577$ |
$0.218854283$ |
3.191239339 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2728\) , \( 55920\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2728{x}+55920$ |
| 12544.2-k2 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.701556175$ |
$1.969688554$ |
3.191239339 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -16\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-8{x}-16$ |
| 12544.2-k3 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{6} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{2} \) |
$2.104668525$ |
$0.656562851$ |
3.191239339 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+72{x}+368$ |
| 12544.2-k4 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{12} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs[2] |
$1$ |
\( 2^{4} \) |
$1.052334262$ |
$0.328281425$ |
3.191239339 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -568\) , \( 4464\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-568{x}+4464$ |
| 12544.2-k5 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{20} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$3.157002788$ |
$0.109427141$ |
3.191239339 |
\( \frac{14378731676028886375}{3256827195820898} a + \frac{9866935598003002000}{1628413597910449} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3680 a + 6632\) , \( 120320 a + 51568\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-3680a+6632\right){x}+120320a+51568$ |
| 12544.2-k6 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{20} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$3.157002788$ |
$0.109427141$ |
3.191239339 |
\( -\frac{14378731676028886375}{3256827195820898} a + \frac{34112602872034890375}{3256827195820898} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3680 a + 2952\) , \( -120320 a + 171888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(3680a+2952\right){x}-120320a+171888$ |
| 12544.2-k7 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$0.350778087$ |
$0.984844277$ |
3.191239339 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -168\) , \( -784\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-168{x}-784$ |
| 12544.2-k8 |
12544.2-k |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{10} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$6.314005577$ |
$0.218854283$ |
3.191239339 |
\( \frac{10722436976428375}{161414428} a + \frac{1349486005943625}{161414428} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3520 a + 6472\) , \( 122880 a + 59760\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-3520a+6472\right){x}+122880a+59760$ |
*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.
