| 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 |
| 1.1-a1 |
1.1-a |
$2$ |
$2$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.53068$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1512.581761$ |
2.696639769 |
\( 1728 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 2 a^{3} - a^{2} - 11 a - 3\) , \( a^{3} + a^{2} - 4 a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(2a^{3}-a^{2}-11a-3\right){x}+a^{3}+a^{2}-4a-3$ |
| 1.1-a2 |
1.1-a |
$2$ |
$2$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.53068$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1512.581761$ |
2.696639769 |
\( 1728 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 2\) , \( 1\) , \( 36 a^{3} - 125 a^{2} + 17 a + 47\) , \( 53 a^{3} - 184 a^{2} + 23 a + 67\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(36a^{3}-125a^{2}+17a+47\right){x}+53a^{3}-184a^{2}+23a+67$ |
| 2.2-a1 |
2.2-a |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{6} \) |
$13.66480$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$1728.672454$ |
0.385235943 |
\( -\frac{6569097003}{8} a^{3} + \frac{2020126797}{2} a^{2} + \frac{19518659343}{4} a + \frac{4249935675}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( -a - 1\) , \( a^{2} - a - 3\) , \( -66 a^{3} + 162 a^{2} + 239 a - 258\) , \( 412 a^{3} - 1048 a^{2} - 1540 a + 1622\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-66a^{3}+162a^{2}+239a-258\right){x}+412a^{3}-1048a^{2}-1540a+1622$ |
| 2.2-a2 |
2.2-a |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{24} \) |
$13.66480$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$108.0420283$ |
0.385235943 |
\( -\frac{8201979}{2048} a^{3} + \frac{16732737}{4096} a^{2} + \frac{3845475}{2048} a + \frac{8397}{2048} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{2} - a - 3\) , \( -a^{3} - 8 a^{2} + 5 a + 22\) , \( -8 a^{3} - 10 a^{2} + 18 a + 22\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-a^{3}-8a^{2}+5a+22\right){x}-8a^{3}-10a^{2}+18a+22$ |
| 2.2-a3 |
2.2-a |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{3} \) |
$13.66480$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$864.3362271$ |
0.385235943 |
\( -\frac{20070242254193687559}{4} a^{3} + \frac{24648740754071220837}{4} a^{2} + 29844247343928311916 a + \frac{26001890461835462781}{2} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -531 a^{3} - 702 a^{2} + 428 a + 331\) , \( 10439 a^{3} + 13438 a^{2} - 8323 a - 6390\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-531a^{3}-702a^{2}+428a+331\right){x}+10439a^{3}+13438a^{2}-8323a-6390$ |
| 2.2-a4 |
2.2-a |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{6} \) |
$13.66480$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$27.01050709$ |
0.385235943 |
\( \frac{12533082656277528963}{8} a^{3} + \frac{4014954980005773159}{2} a^{2} - \frac{4983406353388929987}{4} a - \frac{1909719122581256895}{2} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{2} - 3 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -15 a^{3} + 12 a^{2} + 8 a - 5\) , \( -100 a^{3} + 46 a + 8\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-15a^{3}+12a^{2}+8a-5\right){x}-100a^{3}+46a+8$ |
| 2.2-a5 |
2.2-a |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{12} \) |
$13.66480$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$432.1681135$ |
0.385235943 |
\( \frac{5910872697}{32} a^{3} + \frac{15149919807}{64} a^{2} - \frac{4698905823}{32} a - \frac{3601890693}{32} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{2} - 3 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -3 a^{2} + 3 a\) , \( -a^{3} - 4 a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-3a^{2}+3a\right){x}-a^{3}-4a^{2}+a$ |
| 2.2-a6 |
2.2-a |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{3} \) |
$13.66480$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$864.3362271$ |
0.385235943 |
\( -\frac{22089794375529}{4} a^{3} + \frac{78215202483507}{4} a^{2} - 2515950729072 a - \frac{14336718694641}{2} \) |
\( \bigl[1\) , \( -1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 3 a^{3} - 11 a^{2} + 2 a + 5\) , \( -7 a^{3} + 26 a^{2} - 8 a - 8\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}-{x}^{2}+\left(3a^{3}-11a^{2}+2a+5\right){x}-7a^{3}+26a^{2}-8a-8$ |
| 2.2-b1 |
2.2-b |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{3} \) |
$13.66480$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
|
\( 3 \) |
$1$ |
$55.73864020$ |
2.005930877 |
\( -\frac{22089794375529}{4} a^{3} + \frac{78215202483507}{4} a^{2} - 2515950729072 a - \frac{14336718694641}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( -a - 1\) , \( a + 1\) , \( 3 a^{3} - 12 a^{2} + 2 a + 7\) , \( 7 a^{3} - 26 a^{2} + 7 a + 6\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a^{3}-12a^{2}+2a+7\right){x}+7a^{3}-26a^{2}+7a+6$ |
| 2.2-b2 |
2.2-b |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{3} \) |
$13.66480$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
|
\( 3 \) |
$1$ |
$13.93466005$ |
2.005930877 |
\( -\frac{20070242254193687559}{4} a^{3} + \frac{24648740754071220837}{4} a^{2} + 29844247343928311916 a + \frac{26001890461835462781}{2} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{2} - 2 a - 3\) , \( -529 a^{3} - 711 a^{2} + 433 a + 352\) , \( -11500 a^{3} - 14849 a^{2} + 9190 a + 7070\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-529a^{3}-711a^{2}+433a+352\right){x}-11500a^{3}-14849a^{2}+9190a+7070$ |
| 2.2-b3 |
2.2-b |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{6} \) |
$13.66480$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
|
\( 2 \cdot 3 \) |
$1$ |
$222.9545608$ |
2.005930877 |
\( \frac{12533082656277528963}{8} a^{3} + \frac{4014954980005773159}{2} a^{2} - \frac{4983406353388929987}{4} a - \frac{1909719122581256895}{2} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a + 1\) , \( -16 a^{3} + 7 a^{2} + 25 a + 20\) , \( 70 a^{3} + 18 a^{2} - 18 a + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-16a^{3}+7a^{2}+25a+20\right){x}+70a^{3}+18a^{2}-18a+2$ |
| 2.2-b4 |
2.2-b |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{12} \) |
$13.66480$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
|
\( 2^{2} \cdot 3 \) |
$1$ |
$891.8182432$ |
2.005930877 |
\( \frac{5910872697}{32} a^{3} + \frac{15149919807}{64} a^{2} - \frac{4698905823}{32} a - \frac{3601890693}{32} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a + 1\) , \( -a^{3} - 8 a^{2} + 20 a + 25\) , \( a^{3} - 8 a^{2} + 17 a + 20\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-a^{3}-8a^{2}+20a+25\right){x}+a^{3}-8a^{2}+17a+20$ |
| 2.2-b5 |
2.2-b |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{24} \) |
$13.66480$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
|
\( 2^{3} \cdot 3 \) |
$1$ |
$891.8182432$ |
2.005930877 |
\( -\frac{8201979}{2048} a^{3} + \frac{16732737}{4096} a^{2} + \frac{3845475}{2048} a + \frac{8397}{2048} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{2} - 3 a - 3\) , \( 1\) , \( -3 a^{3} + 2 a^{2} + 3 a + 2\) , \( 3 a^{3} + 6 a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-3a^{3}+2a^{2}+3a+2\right){x}+3a^{3}+6a^{2}-4a-2$ |
| 2.2-b6 |
2.2-b |
$6$ |
$8$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{6} \) |
$13.66480$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
|
\( 2 \cdot 3 \) |
$1$ |
$222.9545608$ |
2.005930877 |
\( -\frac{6569097003}{8} a^{3} + \frac{2020126797}{2} a^{2} + \frac{19518659343}{4} a + \frac{4249935675}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -66 a^{3} + 162 a^{2} + 241 a - 255\) , \( -412 a^{3} + 1048 a^{2} + 1539 a - 1624\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-66a^{3}+162a^{2}+241a-255\right){x}-412a^{3}+1048a^{2}+1539a-1624$ |
| 4.2-a1 |
4.2-a |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$14.90157$ |
$(a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$21.13310665$ |
0.678172110 |
\( \frac{335302240682171}{256} a^{3} - \frac{842442163929297}{256} a^{2} - \frac{77798212163189}{16} a + \frac{654266176789459}{128} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 3 a^{2} + 3 a - 5\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 33 a^{3} - 18 a^{2} - 274 a - 258\) , \( 393 a^{3} - 455 a^{2} - 2692 a - 1630\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-5\right){x}^{2}+\left(33a^{3}-18a^{2}-274a-258\right){x}+393a^{3}-455a^{2}-2692a-1630$ |
| 4.2-a2 |
4.2-a |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.90157$ |
$(a), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$855.8908195$ |
0.678172110 |
\( -\frac{148285}{32} a^{3} + \frac{63593}{4} a^{2} - \frac{10363}{16} a - \frac{40807}{8} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 5 a + 3\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 355 a^{3} - 1265 a^{2} + 181 a + 478\) , \( -8492 a^{3} + 30058 a^{2} - 3840 a - 11008\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+3\right){x}^{2}+\left(355a^{3}-1265a^{2}+181a+478\right){x}-8492a^{3}+30058a^{2}-3840a-11008$ |
| 4.2-a3 |
4.2-a |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.90157$ |
$(a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$10.56655332$ |
0.678172110 |
\( -\frac{1046617536731}{32768} a^{3} + \frac{326816909165}{8192} a^{2} + \frac{3093370051327}{16384} a + \frac{650619737385}{8192} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 5 a + 3\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 3295 a^{3} - 11675 a^{2} + 1521 a + 4293\) , \( 244828 a^{3} - 866893 a^{2} + 111568 a + 317809\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+3\right){x}^{2}+\left(3295a^{3}-11675a^{2}+1521a+4293\right){x}+244828a^{3}-866893a^{2}+111568a+317809$ |
| 4.2-a4 |
4.2-a |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$14.90157$ |
$(a), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1711.781639$ |
0.678172110 |
\( -\frac{201983}{8} a^{3} + \frac{211633}{8} a^{2} + 159765 a + 91008 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a\) , \( -29 a^{3} + 72 a^{2} + 109 a - 111\) , \( -213 a^{3} + 535 a^{2} + 791 a - 831\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-29a^{3}+72a^{2}+109a-111\right){x}-213a^{3}+535a^{2}+791a-831$ |
| 4.2-b1 |
4.2-b |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$14.90157$ |
$(a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 5 \) |
$0.073122178$ |
$562.4574419$ |
2.932937828 |
\( -\frac{201983}{8} a^{3} + \frac{211633}{8} a^{2} + 159765 a + 91008 \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 5 a - 2\) , \( -31 a^{3} + 80 a^{2} + 107 a - 129\) , \( 152 a^{3} - 381 a^{2} - 569 a + 589\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{3}-a^{2}-5a-2\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-31a^{3}+80a^{2}+107a-129\right){x}+152a^{3}-381a^{2}-569a+589$ |
| 4.2-b2 |
4.2-b |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.90157$ |
$(a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.036561089$ |
$562.4574419$ |
2.932937828 |
\( -\frac{148285}{32} a^{3} + \frac{63593}{4} a^{2} - \frac{10363}{16} a - \frac{40807}{8} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 6 a - 2\) , \( a^{2} - 2 a - 3\) , \( 356 a^{3} - 1265 a^{2} + 175 a + 471\) , \( 8847 a^{3} - 31321 a^{2} + 4019 a + 11476\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}^{2}+\left(356a^{3}-1265a^{2}+175a+471\right){x}+8847a^{3}-31321a^{2}+4019a+11476$ |
| 4.2-b3 |
4.2-b |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.90157$ |
$(a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.012187029$ |
$562.4574419$ |
2.932937828 |
\( -\frac{1046617536731}{32768} a^{3} + \frac{326816909165}{8192} a^{2} + \frac{3093370051327}{16384} a + \frac{650619737385}{8192} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 6 a - 2\) , \( a^{2} - 2 a - 3\) , \( 3296 a^{3} - 11675 a^{2} + 1515 a + 4286\) , \( -241533 a^{3} + 855220 a^{2} - 110049 a - 313526\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}^{2}+\left(3296a^{3}-11675a^{2}+1515a+4286\right){x}-241533a^{3}+855220a^{2}-110049a-313526$ |
| 4.2-b4 |
4.2-b |
$4$ |
$6$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$14.90157$ |
$(a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.024374059$ |
$562.4574419$ |
2.932937828 |
\( \frac{335302240682171}{256} a^{3} - \frac{842442163929297}{256} a^{2} - \frac{77798212163189}{16} a + \frac{654266176789459}{128} \) |
\( \bigl[1\) , \( a^{3} - 3 a^{2} - a + 3\) , \( a^{2} - a - 2\) , \( 30 a^{3} - 11 a^{2} - 266 a - 263\) , \( -345 a^{3} + 343 a^{2} + 2369 a + 1565\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(30a^{3}-11a^{2}-266a-263\right){x}-345a^{3}+343a^{2}+2369a+1565$ |
| 5.1-a1 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.419188168$ |
$449.7564671$ |
2.275891063 |
\( -\frac{11848222364}{25} a^{3} + \frac{41952071696}{25} a^{2} - \frac{5398165132}{25} a - \frac{15379225719}{25} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{2} - 2 a - 2\) , \( -255 a^{3} + 636 a^{2} + 954 a - 974\) , \( -3300 a^{3} + 8286 a^{2} + 12260 a - 12855\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(-255a^{3}+636a^{2}+954a-974\right){x}-3300a^{3}+8286a^{2}+12260a-12855$ |
| 5.1-a2 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$2.838376337$ |
$28.10977919$ |
2.275891063 |
\( -\frac{12878820451868344494}{5} a^{3} + \frac{45601128332325683586}{5} a^{2} - \frac{5867411221165505902}{5} a - \frac{16717224412125917979}{5} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{2} - 2 a - 2\) , \( 195 a^{3} - 494 a^{2} - 716 a + 781\) , \( -13563 a^{3} + 34072 a^{2} + 50360 a - 52908\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(195a^{3}-494a^{2}-716a+781\right){x}-13563a^{3}+34072a^{2}+50360a-52908$ |
| 5.1-a3 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.838376337$ |
$449.7564671$ |
2.275891063 |
\( \frac{213085162084933142}{5} a^{3} + \frac{272403773327601867}{5} a^{2} - \frac{169947802951287099}{5} a - \frac{129110855617705053}{5} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a\) , \( a^{2} - 2 a - 2\) , \( 519 a^{3} - 661 a^{2} - 3205 a - 1473\) , \( -11217 a^{3} + 14071 a^{2} + 67599 a + 29718\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a\right){x}^{2}+\left(519a^{3}-661a^{2}-3205a-1473\right){x}-11217a^{3}+14071a^{2}+67599a+29718$ |
| 5.1-a4 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.354797042$ |
$449.7564671$ |
2.275891063 |
\( \frac{105329076}{390625} a^{3} - \frac{187575264}{390625} a^{2} - \frac{525009912}{390625} a + \frac{21361121}{390625} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( 0\) , \( a\) , \( 3 a^{3} - 4 a^{2} - 16 a - 6\) , \( -5 a^{3} + 3 a^{2} + 40 a + 19\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+a{y}={x}^{3}+\left(3a^{3}-4a^{2}-16a-6\right){x}-5a^{3}+3a^{2}+40a+19$ |
| 5.1-a5 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.838376337$ |
$112.4391167$ |
2.275891063 |
\( \frac{235671814}{5} a^{3} - \frac{590807986}{5} a^{2} - \frac{873734178}{5} a + \frac{918039019}{5} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 3 a^{2} - a + 3\) , \( a^{2} - a - 3\) , \( 9 a^{3} - 29 a^{2} - a + 12\) , \( 20 a^{3} - 69 a^{2} + 10 a + 22\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(9a^{3}-29a^{2}-a+12\right){x}+20a^{3}-69a^{2}+10a+22$ |
| 5.1-a6 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.419188168$ |
$1799.025868$ |
2.275891063 |
\( -\frac{34058259661336}{25} a^{3} + \frac{41829584078704}{25} a^{2} + \frac{202581219737332}{25} a + \frac{88249907628119}{25} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -86 a^{3} + 214 a^{2} + 325 a - 337\) , \( 709 a^{3} - 1783 a^{2} - 2629 a + 2766\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-86a^{3}+214a^{2}+325a-337\right){x}+709a^{3}-1783a^{2}-2629a+2766$ |
| 5.1-a7 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.838376337$ |
$449.7564671$ |
2.275891063 |
\( -\frac{69174455073448259030228502}{5} a^{3} + \frac{84954789699914708877643573}{5} a^{2} + \frac{411446861664580628782465339}{5} a + \frac{179237159247146941532397933}{5} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -56 a^{3} + 119 a^{2} + 300 a - 292\) , \( 676 a^{3} - 1582 a^{2} - 3003 a + 2995\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-56a^{3}+119a^{2}+300a-292\right){x}+676a^{3}-1582a^{2}-3003a+2995$ |
| 5.1-a8 |
5.1-a |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.709594084$ |
$1799.025868$ |
2.275891063 |
\( -\frac{270248784}{625} a^{3} + \frac{341881776}{625} a^{2} + \frac{1585344408}{625} a + \frac{689054561}{625} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -6 a^{3} + 14 a^{2} + 25 a - 22\) , \( 12 a^{3} - 33 a^{2} - 36 a + 41\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-6a^{3}+14a^{2}+25a-22\right){x}+12a^{3}-33a^{2}-36a+41$ |
| 5.1-b1 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.258056996$ |
$38.52211070$ |
1.240620741 |
\( -\frac{34058259661336}{25} a^{3} + \frac{41829584078704}{25} a^{2} + \frac{202581219737332}{25} a + \frac{88249907628119}{25} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -84 a^{3} + 208 a^{2} + 319 a - 331\) , \( -794 a^{3} + 1994 a^{2} + 2950 a - 3104\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-84a^{3}+208a^{2}+319a-331\right){x}-794a^{3}+1994a^{2}+2950a-3104$ |
| 5.1-b2 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$4.516113993$ |
$2.407631919$ |
1.240620741 |
\( -\frac{69174455073448259030228502}{5} a^{3} + \frac{84954789699914708877643573}{5} a^{2} + \frac{411446861664580628782465339}{5} a + \frac{179237159247146941532397933}{5} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -54 a^{3} + 113 a^{2} + 294 a - 286\) , \( -731 a^{3} + 1698 a^{2} + 3299 a - 3288\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-54a^{3}+113a^{2}+294a-286\right){x}-731a^{3}+1698a^{2}+3299a-3288$ |
| 5.1-b3 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.129028498$ |
$616.3537713$ |
1.240620741 |
\( -\frac{270248784}{625} a^{3} + \frac{341881776}{625} a^{2} + \frac{1585344408}{625} a + \frac{689054561}{625} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -4 a^{3} + 8 a^{2} + 19 a - 16\) , \( -17 a^{3} + 44 a^{2} + 57 a - 64\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-4a^{3}+8a^{2}+19a-16\right){x}-17a^{3}+44a^{2}+57a-64$ |
| 5.1-b4 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.282257124$ |
$2465.415085$ |
1.240620741 |
\( \frac{235671814}{5} a^{3} - \frac{590807986}{5} a^{2} - \frac{873734178}{5} a + \frac{918039019}{5} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{2} - 2 a - 4\) , \( a\) , \( 7 a^{3} - 27 a^{2} + 9 a + 12\) , \( -24 a^{3} + 85 a^{2} - 12 a - 29\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(7a^{3}-27a^{2}+9a+12\right){x}-24a^{3}+85a^{2}-12a-29$ |
| 5.1-b5 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.564514249$ |
$154.0884428$ |
1.240620741 |
\( \frac{105329076}{390625} a^{3} - \frac{187575264}{390625} a^{2} - \frac{525009912}{390625} a + \frac{21361121}{390625} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( 2 a^{3} - 2 a^{2} - 6 a + 2\) , \( 12 a^{3} - 10 a^{2} - 76 a - 33\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(2a^{3}-2a^{2}-6a+2\right){x}+12a^{3}-10a^{2}-76a-33$ |
| 5.1-b6 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$4.516113993$ |
$2.407631919$ |
1.240620741 |
\( \frac{213085162084933142}{5} a^{3} + \frac{272403773327601867}{5} a^{2} - \frac{169947802951287099}{5} a - \frac{129110855617705053}{5} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 524 a^{3} - 666 a^{2} - 3239 a - 1491\) , \( 14271 a^{3} - 17992 a^{2} - 86048 a - 37666\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(524a^{3}-666a^{2}-3239a-1491\right){x}+14271a^{3}-17992a^{2}-86048a-37666$ |
| 5.1-b7 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.564514249$ |
$2465.415085$ |
1.240620741 |
\( -\frac{11848222364}{25} a^{3} + \frac{41952071696}{25} a^{2} - \frac{5398165132}{25} a - \frac{15379225719}{25} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 7 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -254 a^{3} + 636 a^{2} + 945 a - 977\) , \( 3046 a^{3} - 7651 a^{2} - 11312 a + 11878\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-1\right){x}^{2}+\left(-254a^{3}+636a^{2}+945a-977\right){x}+3046a^{3}-7651a^{2}-11312a+11878$ |
| 5.1-b8 |
5.1-b |
$8$ |
$16$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.32307$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.129028498$ |
$616.3537713$ |
1.240620741 |
\( -\frac{12878820451868344494}{5} a^{3} + \frac{45601128332325683586}{5} a^{2} - \frac{5867411221165505902}{5} a - \frac{16717224412125917979}{5} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 7 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 196 a^{3} - 494 a^{2} - 725 a + 778\) , \( 13759 a^{3} - 34567 a^{2} - 51082 a + 53686\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-1\right){x}^{2}+\left(196a^{3}-494a^{2}-725a+778\right){x}+13759a^{3}-34567a^{2}-51082a+53686$ |
| 7.1-a1 |
7.1-a |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1117.868436$ |
1.992942504 |
\( -\frac{39861}{7} a^{3} + 10127 a^{2} + \frac{159972}{7} a + \frac{130637}{7} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{2} - 3 a - 4\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -21 a^{3} + 53 a^{2} + 74 a - 78\) , \( 78 a^{3} - 194 a^{2} - 294 a + 295\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(-21a^{3}+53a^{2}+74a-78\right){x}+78a^{3}-194a^{2}-294a+295$ |
| 7.1-a2 |
7.1-a |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2235.736873$ |
1.992942504 |
\( \frac{32964}{49} a^{3} - \frac{11896}{7} a^{2} - \frac{132816}{49} a + \frac{265215}{49} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a\) , \( -2 a^{2} + 3\) , \( -a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(-2a^{2}+3\right){x}-a$ |
| 7.1-a3 |
7.1-a |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$558.9342183$ |
1.992942504 |
\( \frac{12357992448}{2401} a^{3} - \frac{4458086057}{343} a^{2} - \frac{48099423903}{2401} a + \frac{57423244385}{2401} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a\) , \( -17 a^{2} + 5 a + 8\) , \( -29 a^{3} + 12 a^{2} + 11 a - 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(-17a^{2}+5a+8\right){x}-29a^{3}+12a^{2}+11a-3$ |
| 7.1-a4 |
7.1-a |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1117.868436$ |
1.992942504 |
\( \frac{161885}{7} a^{3} + 30128 a^{2} - \frac{125483}{7} a - \frac{95469}{7} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 6 a + 3\) , \( 0\) , \( -3 a^{3} + 4 a^{2} + 17 a + 8\) , \( -3 a^{3} + 4 a^{2} + 17 a + 7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{3}+a^{2}+6a+3\right){x}^{2}+\left(-3a^{3}+4a^{2}+17a+8\right){x}-3a^{3}+4a^{2}+17a+7$ |
| 7.1-b1 |
7.1-b |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.804881705$ |
$474.5183701$ |
2.723636549 |
\( \frac{161885}{7} a^{3} + 30128 a^{2} - \frac{125483}{7} a - \frac{95469}{7} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{2} - a - 3\) , \( -a^{3} + 2 a^{2} + 3 a + 1\) , \( a^{3} - a^{2} - 7 a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-2\right){x}^{2}+\left(-a^{3}+2a^{2}+3a+1\right){x}+a^{3}-a^{2}-7a-3$ |
| 7.1-b2 |
7.1-b |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.402440852$ |
$1898.073480$ |
2.723636549 |
\( \frac{32964}{49} a^{3} - \frac{11896}{7} a^{2} - \frac{132816}{49} a + \frac{265215}{49} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 3 a + 4\) , \( -a^{3} + 5 a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(-a^{3}+3a+4\right){x}-a^{3}+5a+1$ |
| 7.1-b3 |
7.1-b |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.201220426$ |
$474.5183701$ |
2.723636549 |
\( \frac{12357992448}{2401} a^{3} - \frac{4458086057}{343} a^{2} - \frac{48099423903}{2401} a + \frac{57423244385}{2401} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} - 15 a^{2} + 8 a + 9\) , \( 28 a^{3} - 27 a^{2} - 2 a + 9\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(-a^{3}-15a^{2}+8a+9\right){x}+28a^{3}-27a^{2}-2a+9$ |
| 7.1-b4 |
7.1-b |
$4$ |
$4$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$15.98129$ |
$(a^3-2a^2-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.201220426$ |
$1898.073480$ |
2.723636549 |
\( -\frac{39861}{7} a^{3} + 10127 a^{2} + \frac{159972}{7} a + \frac{130637}{7} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( a^{2} - a - 2\) , \( -20 a^{3} + 47 a^{2} + 78 a - 66\) , \( -98 a^{3} + 243 a^{2} + 368 a - 369\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}^{2}+\left(-20a^{3}+47a^{2}+78a-66\right){x}-98a^{3}+243a^{2}+368a-369$ |
| 8.3-a1 |
8.3-a |
$1$ |
$1$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.25028$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$4$ |
\( 2^{2} \) |
$1$ |
$24.76366276$ |
2.825523547 |
\( -209920 a^{3} + 255744 a^{2} + 571392 a - 497920 \) |
\( \bigl[0\) , \( a^{3} - 3 a^{2} - a + 3\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -165 a^{3} + 416 a^{2} + 608 a - 642\) , \( -1962 a^{3} + 4929 a^{2} + 7286 a - 7660\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(-165a^{3}+416a^{2}+608a-642\right){x}-1962a^{3}+4929a^{2}+7286a-7660$ |
| 8.3-b1 |
8.3-b |
$1$ |
$1$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.25028$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.095429650$ |
$611.1638008$ |
3.327323384 |
\( 46080 a^{3} - 161024 a^{2} + 16384 a + 51968 \) |
\( \bigl[0\) , \( a^{3} - 3 a^{2} - a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 16 a^{3} - 20 a^{2} - 94 a - 34\) , \( -53 a^{3} + 65 a^{2} + 316 a + 138\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+5\right){x}^{2}+\left(16a^{3}-20a^{2}-94a-34\right){x}-53a^{3}+65a^{2}+316a+138$ |
| 8.3-c1 |
8.3-c |
$1$ |
$1$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.25028$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.227481585$ |
$394.8608628$ |
5.124416150 |
\( 768 a^{2} - 1024 a - 3328 \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 5 a\) , \( a^{2} - 2 a - 2\) , \( -35 a^{3} + 87 a^{2} + 132 a - 131\) , \( -245 a^{3} + 616 a^{2} + 909 a - 961\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a\right){x}^{2}+\left(-35a^{3}+87a^{2}+132a-131\right){x}-245a^{3}+616a^{2}+909a-961$ |
| 8.3-d1 |
8.3-d |
$1$ |
$1$ |
4.4.19664.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.25028$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.042027207$ |
$533.4422787$ |
1.279004365 |
\( 768 a^{2} - 1024 a - 3328 \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -35 a^{3} + 87 a^{2} + 132 a - 131\) , \( 245 a^{3} - 616 a^{2} - 909 a + 958\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a\right){x}^{2}+\left(-35a^{3}+87a^{2}+132a-131\right){x}+245a^{3}-616a^{2}-909a+958$ |
*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.
