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 |
4.1-a1 |
4.1-a |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$114.7100900$ |
0.815291469 |
\( \frac{41230058349407477209904451719}{4096} a^{3} - \frac{94246334519813332521722070655}{4096} a^{2} - \frac{167422374788299075786050167801}{4096} a + \frac{256512578292996597693430067855}{4096} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 4 a + 7\) , \( a^{2} - a - 4\) , \( 77 a^{3} + 17 a^{2} - 533 a - 602\) , \( 1024 a^{3} + 170 a^{2} - 6987 a - 7004\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+7\right){x}^{2}+\left(77a^{3}+17a^{2}-533a-602\right){x}+1024a^{3}+170a^{2}-6987a-7004$ |
4.1-a2 |
4.1-a |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$114.7100900$ |
0.815291469 |
\( -\frac{2346047242153}{16} a^{3} - \frac{376327635191}{16} a^{2} + \frac{15992303386463}{16} a + \frac{16204332806527}{16} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 4 a + 7\) , \( a^{2} - a - 4\) , \( 82 a^{3} + 7 a^{2} - 558 a - 547\) , \( 1059 a^{3} + 165 a^{2} - 7221 a - 7303\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+7\right){x}^{2}+\left(82a^{3}+7a^{2}-558a-547\right){x}+1059a^{3}+165a^{2}-7221a-7303$ |
4.1-a3 |
4.1-a |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$114.7100900$ |
0.815291469 |
\( \frac{26222529}{256} a^{3} + \frac{6267319}{256} a^{2} - \frac{181417919}{256} a - \frac{192705095}{256} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 4 a + 7\) , \( a^{2} - a - 4\) , \( 7 a^{3} - 3 a^{2} - 43 a - 27\) , \( 20 a^{3} + a^{2} - 134 a - 127\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+7\right){x}^{2}+\left(7a^{3}-3a^{2}-43a-27\right){x}+20a^{3}+a^{2}-134a-127$ |
4.1-a4 |
4.1-a |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$114.7100900$ |
0.815291469 |
\( -\frac{22620233475289479327}{16777216} a^{3} + \frac{51706792967840493911}{16777216} a^{2} + \frac{91853695059136217057}{16777216} a - \frac{140731656537155986407}{16777216} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 4 a + 7\) , \( a^{2} - a - 4\) , \( -3 a^{3} - 3 a^{2} + 27 a + 38\) , \( 64 a^{3} + 10 a^{2} - 439 a - 444\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+7\right){x}^{2}+\left(-3a^{3}-3a^{2}+27a+38\right){x}+64a^{3}+10a^{2}-439a-444$ |
4.1-b1 |
4.1-b |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$7.685844052$ |
0.491637900 |
\( \frac{41230058349407477209904451719}{4096} a^{3} - \frac{94246334519813332521722070655}{4096} a^{2} - \frac{167422374788299075786050167801}{4096} a + \frac{256512578292996597693430067855}{4096} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( -637 a^{3} + 1422 a^{2} + 2717 a - 4074\) , \( -18410 a^{3} + 41809 a^{2} + 75873 a - 115460\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+8\right){x}^{2}+\left(-637a^{3}+1422a^{2}+2717a-4074\right){x}-18410a^{3}+41809a^{2}+75873a-115460$ |
4.1-b2 |
4.1-b |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{36} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$7.685844052$ |
0.491637900 |
\( -\frac{22620233475289479327}{16777216} a^{3} + \frac{51706792967840493911}{16777216} a^{2} + \frac{91853695059136217057}{16777216} a - \frac{140731656537155986407}{16777216} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( -37 a^{3} + 82 a^{2} + 157 a - 234\) , \( -378 a^{3} + 857 a^{2} + 1561 a - 2372\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+8\right){x}^{2}+\left(-37a^{3}+82a^{2}+157a-234\right){x}-378a^{3}+857a^{2}+1561a-2372$ |
4.1-b3 |
4.1-b |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$622.5533682$ |
0.491637900 |
\( -\frac{2346047242153}{16} a^{3} - \frac{376327635191}{16} a^{2} + \frac{15992303386463}{16} a + \frac{16204332806527}{16} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( -2 a^{3} + 2 a^{2} + 12 a - 19\) , \( -48 a^{3} + 111 a^{2} + 189 a - 290\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+8\right){x}^{2}+\left(-2a^{3}+2a^{2}+12a-19\right){x}-48a^{3}+111a^{2}+189a-290$ |
4.1-b4 |
4.1-b |
$4$ |
$6$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$14.95150$ |
$(-a^2+2), (a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$622.5533682$ |
0.491637900 |
\( \frac{26222529}{256} a^{3} + \frac{6267319}{256} a^{2} - \frac{181417919}{256} a - \frac{192705095}{256} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( 3 a^{3} - 8 a^{2} - 13 a + 21\) , \( 2 a^{3} - 5 a^{2} - 9 a + 14\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+8\right){x}^{2}+\left(3a^{3}-8a^{2}-13a+21\right){x}+2a^{3}-5a^{2}-9a+14$ |
8.2-a1 |
8.2-a |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$238.7216505$ |
0.848346144 |
\( -647854964733 a^{3} + 1827483746307 a^{2} + 1207461593061 a - 2846428036393 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -30 a^{3} + 70 a^{2} + 121 a - 193\) , \( 127 a^{3} - 292 a^{2} - 515 a + 797\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-30a^{3}+70a^{2}+121a-193\right){x}+127a^{3}-292a^{2}-515a+797$ |
8.2-a2 |
8.2-a |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$238.7216505$ |
0.848346144 |
\( 291693 a^{3} - 823209 a^{2} - 542979 a + 1283033 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( a + 2\) , \( 4 a^{3} - 9 a^{2} - 17 a + 23\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a+2\right){x}+4a^{3}-9a^{2}-17a+23$ |
8.2-b1 |
8.2-b |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$437.9142580$ |
1.556217760 |
\( 60777693184 a^{3} + 118359425023 a^{2} - 76589727738 a - 164965055753 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -549 a^{3} + 1260 a^{2} + 2225 a - 3448\) , \( 9759 a^{3} - 22321 a^{2} - 39615 a + 60789\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-549a^{3}+1260a^{2}+2225a-3448\right){x}+9759a^{3}-22321a^{2}-39615a+60789$ |
8.2-b2 |
8.2-b |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$437.9142580$ |
1.556217760 |
\( -40971 a^{3} - 79859 a^{2} + 51379 a + 111001 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( 11 a^{3} - 25 a^{2} - 45 a + 67\) , \( 606 a^{3} - 1386 a^{2} - 2460 a + 3772\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(11a^{3}-25a^{2}-45a+67\right){x}+606a^{3}-1386a^{2}-2460a+3772$ |
8.2-c1 |
8.2-c |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.096139965$ |
$451.4536406$ |
1.758573213 |
\( -63 a^{3} - 361 a^{2} - 223 a + 185 \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -a^{2} + 6 a + 14\) , \( -a^{3} + 3 a^{2} + 10 a + 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(-a^{2}+6a+14\right){x}-a^{3}+3a^{2}+10a+2$ |
8.2-c2 |
8.2-c |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.384559860$ |
$56.43170507$ |
1.758573213 |
\( -231484538691 a^{3} + 81225253125 a^{2} + 1381429690059 a + 1149868245473 \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a^{2} + 3 a - 9\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -309 a^{3} + 693 a^{2} + 1308 a - 1964\) , \( -2962 a^{3} + 6697 a^{2} + 12334 a - 18690\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-9\right){x}^{2}+\left(-309a^{3}+693a^{2}+1308a-1964\right){x}-2962a^{3}+6697a^{2}+12334a-18690$ |
8.2-c3 |
8.2-c |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$8.769119721$ |
$3.526981567$ |
1.758573213 |
\( -479610779087949252847104 a^{3} - 76389682012768643160953 a^{2} + 3268718856736807535342218 a + 3309731059747175524850139 \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a^{2} + 3 a - 9\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 971 a^{3} - 2222 a^{2} - 3902 a + 5941\) , \( -27072 a^{3} + 61837 a^{2} + 110206 a - 168840\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-9\right){x}^{2}+\left(971a^{3}-2222a^{2}-3902a+5941\right){x}-27072a^{3}+61837a^{2}+110206a-168840$ |
8.2-c4 |
8.2-c |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.192279930$ |
$902.9072812$ |
1.758573213 |
\( 786429 a^{3} + 2072583 a^{2} - 286707 a - 2096407 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - 3\) , \( a + 1\) , \( 34 a^{3} - 91 a^{2} - 71 a + 138\) , \( 193 a^{3} - 540 a^{2} - 367 a + 834\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(34a^{3}-91a^{2}-71a+138\right){x}+193a^{3}-540a^{2}-367a+834$ |
8.2-c5 |
8.2-c |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.096139965$ |
$902.9072812$ |
1.758573213 |
\( 34326784622403 a^{3} + 66847882281211 a^{2} - 43257982762187 a - 93170180094993 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - 3\) , \( a + 1\) , \( 44 a^{3} - 121 a^{2} - 91 a + 183\) , \( 60 a^{3} - 168 a^{2} - 115 a + 260\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(44a^{3}-121a^{2}-91a+183\right){x}+60a^{3}-168a^{2}-115a+260$ |
8.2-c6 |
8.2-c |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$8.769119721$ |
$3.526981567$ |
1.758573213 |
\( -11937356969141879711232 a^{3} + 33673162453713112189817 a^{2} + 22248654488871995695478 a - 52448202670886652855307 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - 3\) , \( a + 1\) , \( 8084 a^{3} - 22746 a^{2} - 15161 a + 35308\) , \( 769517 a^{3} - 2170362 a^{2} - 1434724 a + 3379800\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(8084a^{3}-22746a^{2}-15161a+35308\right){x}+769517a^{3}-2170362a^{2}-1434724a+3379800$ |
8.2-d1 |
8.2-d |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$327.4718755$ |
1.163738196 |
\( -40971 a^{3} - 79859 a^{2} + 51379 a + 111001 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -6 a^{3} + 18 a^{2} + 7 a - 23\) , \( 224 a^{3} - 631 a^{2} - 422 a + 988\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-6a^{3}+18a^{2}+7a-23\right){x}+224a^{3}-631a^{2}-422a+988$ |
8.2-d2 |
8.2-d |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$327.4718755$ |
1.163738196 |
\( 60777693184 a^{3} + 118359425023 a^{2} - 76589727738 a - 164965055753 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( 234 a^{3} - 657 a^{2} - 443 a + 1022\) , \( 3299 a^{3} - 9304 a^{2} - 6153 a + 14489\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(234a^{3}-657a^{2}-443a+1022\right){x}+3299a^{3}-9304a^{2}-6153a+14489$ |
8.2-e1 |
8.2-e |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.402744617$ |
$481.3990647$ |
2.399745218 |
\( -63 a^{3} - 361 a^{2} - 223 a + 185 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 10\) , \( -20 a^{3} + 49 a^{2} + 80 a - 134\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(2a^{3}-3a^{2}-8a+10\right){x}-20a^{3}+49a^{2}+80a-134$ |
8.2-e2 |
8.2-e |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.701372308$ |
$240.6995323$ |
2.399745218 |
\( -479610779087949252847104 a^{3} - 76389682012768643160953 a^{2} + 3268718856736807535342218 a + 3309731059747175524850139 \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( 5953 a^{3} - 16785 a^{2} - 11105 a + 26137\) , \( -488806 a^{3} + 1378826 a^{2} + 911048 a - 2147590\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(5953a^{3}-16785a^{2}-11105a+26137\right){x}-488806a^{3}+1378826a^{2}+911048a-2147590$ |
8.2-e3 |
8.2-e |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.701372308$ |
$240.6995323$ |
2.399745218 |
\( -11937356969141879711232 a^{3} + 33673162453713112189817 a^{2} + 22248654488871995695478 a - 52448202670886652855307 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 13 a^{3} + 86 a^{2} - 131 a - 693\) , \( -324 a^{3} - 658 a^{2} + 2611 a + 6314\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(13a^{3}+86a^{2}-131a-693\right){x}-324a^{3}-658a^{2}+2611a+6314$ |
8.2-e4 |
8.2-e |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.350686154$ |
$962.7981294$ |
2.399745218 |
\( -231484538691 a^{3} + 81225253125 a^{2} + 1381429690059 a + 1149868245473 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 53 a^{3} + 11 a^{2} - 361 a - 388\) , \( -613 a^{3} - 90 a^{2} + 4166 a + 4196\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(53a^{3}+11a^{2}-361a-388\right){x}-613a^{3}-90a^{2}+4166a+4196$ |
8.2-e5 |
8.2-e |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.402744617$ |
$60.17488308$ |
2.399745218 |
\( 34326784622403 a^{3} + 66847882281211 a^{2} - 43257982762187 a - 93170180094993 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( a + 1\) , \( -27 a^{3} + 71 a^{2} + 99 a - 218\) , \( -237 a^{3} + 520 a^{2} + 986 a - 1360\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-27a^{3}+71a^{2}+99a-218\right){x}-237a^{3}+520a^{2}+986a-1360$ |
8.2-e6 |
8.2-e |
$6$ |
$8$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$16.30473$ |
$(a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.701372308$ |
$962.7981294$ |
2.399745218 |
\( 786429 a^{3} + 2072583 a^{2} - 286707 a - 2096407 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 3 a^{3} + a^{2} - 21 a - 23\) , \( -17 a^{3} + 10 a^{2} + 101 a + 48\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(3a^{3}+a^{2}-21a-23\right){x}-17a^{3}+10a^{2}+101a+48$ |
8.2-f1 |
8.2-f |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$915.7021625$ |
3.254134667 |
\( 291693 a^{3} - 823209 a^{2} - 542979 a + 1283033 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( -a^{2} + 2 a + 5\) , \( 0\) , \( 2 a^{3} - 7 a^{2} - 4 a + 24\) , \( -a^{2} + 11\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(2a^{3}-7a^{2}-4a+24\right){x}-a^{2}+11$ |
8.2-f2 |
8.2-f |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$16.30473$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$915.7021625$ |
3.254134667 |
\( -647854964733 a^{3} + 1827483746307 a^{2} + 1207461593061 a - 2846428036393 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( -a^{2} + 2 a + 5\) , \( 0\) , \( 12 a^{3} - 37 a^{2} - 24 a + 69\) , \( -44 a^{3} + 126 a^{2} + 80 a - 190\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(12a^{3}-37a^{2}-24a+69\right){x}-44a^{3}+126a^{2}+80a-190$ |
10.2-a1 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.137508209$ |
$1860.615168$ |
5.455288409 |
\( \frac{281894497}{1600} a^{3} - \frac{641073513}{1600} a^{2} - \frac{232768723}{320} a + \frac{1784392217}{1600} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 27 a^{3} - 81 a^{2} - 43 a + 139\) , \( -152 a^{3} + 424 a^{2} + 292 a - 653\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(27a^{3}-81a^{2}-43a+139\right){x}-152a^{3}+424a^{2}+292a-653$ |
10.2-a2 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{4} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.275016418$ |
$465.1537920$ |
5.455288409 |
\( \frac{926146356449381}{5000} a^{3} - \frac{2117094157744749}{5000} a^{2} - \frac{752147055461879}{1000} a + \frac{5762277566448941}{5000} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 62 a^{3} - 171 a^{2} - 123 a + 259\) , \( 292 a^{3} - 776 a^{2} - 623 a + 1099\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(62a^{3}-171a^{2}-123a+259\right){x}+292a^{3}-776a^{2}-623a+1099$ |
10.2-a3 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.275016418$ |
$930.3075841$ |
5.455288409 |
\( \frac{15407}{40} a^{3} - \frac{28903}{40} a^{2} - \frac{11053}{8} a + \frac{88207}{40} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 4\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -5 a^{3} + 18 a^{2} + 25 a - 46\) , \( 10 a^{3} - 11 a^{2} - 32 a + 36\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-5a^{3}+18a^{2}+25a-46\right){x}+10a^{3}-11a^{2}-32a+36$ |
10.2-a4 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.068754104$ |
$930.3075841$ |
5.455288409 |
\( -\frac{5953141884539}{20480} a^{3} + \frac{16793324164371}{20480} a^{2} + \frac{2219102602241}{4096} a - \frac{26156605672419}{20480} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -8 a^{3} - 31 a^{2} + 53\) , \( -90 a^{3} - 191 a^{2} + 103 a + 277\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+5\right){x}{y}+\left(a^{3}-2a^{2}-4a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+8\right){x}^{2}+\left(-8a^{3}-31a^{2}+53\right){x}-90a^{3}-191a^{2}+103a+277$ |
10.2-b1 |
10.2-b |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.064527244$ |
$1310.109571$ |
1.201688798 |
\( \frac{92624126421}{200} a^{3} + \frac{180375975491}{200} a^{2} - \frac{23344659439}{40} a - \frac{251401484819}{200} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a\) , \( -39 a^{3} + 104 a^{2} + 82 a - 147\) , \( 133 a^{3} - 381 a^{2} - 239 a + 605\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-39a^{3}+104a^{2}+82a-147\right){x}+133a^{3}-381a^{2}-239a+605$ |
10.2-b2 |
10.2-b |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.032263622$ |
$2620.219142$ |
1.201688798 |
\( \frac{5241983837}{320} a^{3} - \frac{12000242053}{320} a^{2} - \frac{4254963207}{64} a + \frac{32693132597}{320} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - a^{2} - 5 a\) , \( 6 a^{3} - 12 a^{2} - 27 a + 26\) , \( 6 a^{3} - 15 a^{2} - 23 a + 44\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(6a^{3}-12a^{2}-27a+26\right){x}+6a^{3}-15a^{2}-23a+44$ |
10.2-c1 |
10.2-c |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$793.0373736$ |
2.818220285 |
\( \frac{156555109}{50} a^{3} - \frac{357773261}{50} a^{2} - \frac{127029151}{10} a + \frac{973277949}{50} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} - a - 3\) , \( -8 a^{2} + 16 a + 18\) , \( 13 a^{3} - 42 a^{2} - 22 a + 95\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-8a^{2}+16a+18\right){x}+13a^{3}-42a^{2}-22a+95$ |
10.2-c2 |
10.2-c |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$793.0373736$ |
2.818220285 |
\( -\frac{2410883683}{20} a^{3} + \frac{6800672827}{20} a^{2} + \frac{898669113}{4} a - \frac{10592430283}{20} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 1\) , \( a^{3} + a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+{x}+a^{3}+a^{2}-3a-3$ |
10.2-d1 |
10.2-d |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{14} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.261515903$ |
$59.10421161$ |
3.075996537 |
\( \frac{29263792417871110513}{390625000000} a^{3} - \frac{66892456727166401977}{390625000000} a^{2} - \frac{23766272438515846467}{78125000000} a + \frac{182062010179875460393}{390625000000} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 3 a^{2} + 3 a - 7\) , \( a^{3} - a^{2} - 5 a\) , \( -8 a^{3} + 19 a^{2} + 32 a - 58\) , \( 56 a^{3} - 136 a^{2} - 197 a + 316\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-7\right){x}^{2}+\left(-8a^{3}+19a^{2}+32a-58\right){x}+56a^{3}-136a^{2}-197a+316$ |
10.2-d2 |
10.2-d |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{7} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 7 \) |
$0.523031807$ |
$118.2084232$ |
3.075996537 |
\( -\frac{1267618337281}{625000} a^{3} + \frac{488374808849}{625000} a^{2} + \frac{2101610388979}{125000} a + \frac{9997063509159}{625000} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a\) , \( -97 a^{3} - 193 a^{2} + 110 a + 257\) , \( -2269 a^{3} - 4424 a^{2} + 2845 a + 6149\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(-97a^{3}-193a^{2}+110a+257\right){x}-2269a^{3}-4424a^{2}+2845a+6149$ |
10.2-e1 |
10.2-e |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{7} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$540.3329937$ |
0.960091828 |
\( -\frac{1267618337281}{625000} a^{3} + \frac{488374808849}{625000} a^{2} + \frac{2101610388979}{125000} a + \frac{9997063509159}{625000} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 8\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -33 a^{3} - 27 a^{2} + 66 a + 10\) , \( 222 a^{3} + 633 a^{2} - 148 a - 1028\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+8\right){x}^{2}+\left(-33a^{3}-27a^{2}+66a+10\right){x}+222a^{3}+633a^{2}-148a-1028$ |
10.2-e2 |
10.2-e |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{14} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$135.0832484$ |
0.960091828 |
\( \frac{29263792417871110513}{390625000000} a^{3} - \frac{66892456727166401977}{390625000000} a^{2} - \frac{23766272438515846467}{78125000000} a + \frac{182062010179875460393}{390625000000} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( 3 a^{3} - 23 a - 23\) , \( -16 a^{3} - 2 a^{2} + 107 a + 105\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(3a^{3}-23a-23\right){x}-16a^{3}-2a^{2}+107a+105$ |
10.2-f1 |
10.2-f |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.529285205$ |
$504.9325672$ |
3.798957290 |
\( \frac{156555109}{50} a^{3} - \frac{357773261}{50} a^{2} - \frac{127029151}{10} a + \frac{973277949}{50} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 3 a^{2} - 4 a + 7\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( 2 a^{3} - 8 a^{2} - 5 a + 28\) , \( 2 a^{3} - 7 a^{2} - 7 a + 25\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+7\right){x}^{2}+\left(2a^{3}-8a^{2}-5a+28\right){x}+2a^{3}-7a^{2}-7a+25$ |
10.2-f2 |
10.2-f |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.264642602$ |
$1009.865134$ |
3.798957290 |
\( -\frac{2410883683}{20} a^{3} + \frac{6800672827}{20} a^{2} + \frac{898669113}{4} a - \frac{10592430283}{20} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( 0\) , \( -5 a^{3} - 12 a^{2} - 3 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}-5a^{3}-12a^{2}-3a+4$ |
10.2-g1 |
10.2-g |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$142.4456807$ |
0.506209821 |
\( \frac{92624126421}{200} a^{3} + \frac{180375975491}{200} a^{2} - \frac{23344659439}{40} a - \frac{251401484819}{200} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 3 a^{2} - 2 a + 9\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -46 a^{3} + 102 a^{2} + 191 a - 263\) , \( -378 a^{3} + 861 a^{2} + 1540 a - 2335\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+9\right){x}^{2}+\left(-46a^{3}+102a^{2}+191a-263\right){x}-378a^{3}+861a^{2}+1540a-2335$ |
10.2-g2 |
10.2-g |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$142.4456807$ |
0.506209821 |
\( \frac{5241983837}{320} a^{3} - \frac{12000242053}{320} a^{2} - \frac{4254963207}{64} a + \frac{32693132597}{320} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -6 a^{3} + 16 a^{2} + 30 a - 45\) , \( -18 a^{3} + 45 a^{2} + 74 a - 119\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-6a^{3}+16a^{2}+30a-45\right){x}-18a^{3}+45a^{2}+74a-119$ |
10.2-h1 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$684.5604225$ |
3.649087925 |
\( \frac{15407}{40} a^{3} - \frac{28903}{40} a^{2} - \frac{11053}{8} a + \frac{88207}{40} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{3} + 2 a^{2} - 4 a - 8\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(a^{3}+a^{2}-4a-4\right){x}+a^{3}+2a^{2}-4a-8$ |
10.2-h2 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$171.1401056$ |
3.649087925 |
\( -\frac{5953141884539}{20480} a^{3} + \frac{16793324164371}{20480} a^{2} + \frac{2219102602241}{4096} a - \frac{26156605672419}{20480} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{2} - a - 4\) , \( -23 a^{3} + 43 a^{2} + 87 a - 122\) , \( -176 a^{3} + 416 a^{2} + 724 a - 1124\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(-23a^{3}+43a^{2}+87a-122\right){x}-176a^{3}+416a^{2}+724a-1124$ |
10.2-h3 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{4} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$171.1401056$ |
3.649087925 |
\( \frac{926146356449381}{5000} a^{3} - \frac{2117094157744749}{5000} a^{2} - \frac{752147055461879}{1000} a + \frac{5762277566448941}{5000} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( -66 a^{3} + 178 a^{2} + 244 a - 545\) , \( -825 a^{3} + 1810 a^{2} + 3445 a - 4709\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-66a^{3}+178a^{2}+244a-545\right){x}-825a^{3}+1810a^{2}+3445a-4709$ |
10.2-h4 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$684.5604225$ |
3.649087925 |
\( \frac{281894497}{1600} a^{3} - \frac{641073513}{1600} a^{2} - \frac{232768723}{320} a + \frac{1784392217}{1600} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( -a^{3} + 8 a^{2} + 4 a - 25\) , \( -17 a^{3} + 44 a^{2} + 73 a - 117\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-a^{3}+8a^{2}+4a-25\right){x}-17a^{3}+44a^{2}+73a-117$ |
16.1-a1 |
16.1-a |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.78043$ |
$(-a^2+2), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.416906484$ |
$70.79930984$ |
2.851947199 |
\( -\frac{900159}{16} a^{3} + \frac{2061239}{16} a^{2} + \frac{3651137}{16} a - \frac{5619783}{16} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 0\) , \( -2 a^{2} - a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}-2a^{2}-a+2$ |
16.1-a2 |
16.1-a |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$17.78043$ |
$(-a^2+2), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.708453242$ |
$70.79930984$ |
2.851947199 |
\( \frac{70671597575}{4} a^{3} - \frac{161548206103}{4} a^{2} - \frac{286972379153}{4} a + \frac{439696755743}{4} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -15 a^{2} + 20\) , \( -9 a^{3} - 63 a^{2} + 6 a + 90\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-15a^{2}+20\right){x}-9a^{3}-63a^{2}+6a+90$ |
*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.