| 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 |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$37.80891$ |
$\textsf{none}$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.017072839$ |
$17159.21048$ |
0.865480808 |
\( -21722456100 a^{4} - 12368748640 a^{3} + 166738067484 a^{2} + 94941724736 a - 76283378968 \) |
\( \bigl[5 a^{4} + 3 a^{3} - 39 a^{2} - 23 a + 22\) , \( 6 a^{4} + 3 a^{3} - 46 a^{2} - 25 a + 22\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 15 a + 17\) , \( -9 a^{4} - 9 a^{3} + 39 a^{2} + 17 a - 15\) , \( 39 a^{4} + 97 a^{3} - 36 a^{2} - 79 a + 32\bigr] \) |
${y}^2+\left(5a^{4}+3a^{3}-39a^{2}-23a+22\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-15a+17\right){y}={x}^{3}+\left(6a^{4}+3a^{3}-46a^{2}-25a+22\right){x}^{2}+\left(-9a^{4}-9a^{3}+39a^{2}+17a-15\right){x}+39a^{4}+97a^{3}-36a^{2}-79a+32$ |
| 1.1-a2 |
1.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$37.80891$ |
$\textsf{none}$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$0.034145678$ |
$34318.42097$ |
0.865480808 |
\( -2128 a^{4} + 256032 a^{3} + 858688 a^{2} + 309056 a - 335168 \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -5 a^{4} - 2 a^{3} + 38 a^{2} + 16 a - 18\) , \( 1\) , \( -17 a^{4} - 8 a^{3} + 132 a^{2} + 62 a - 69\) , \( 20 a^{4} + 9 a^{3} - 156 a^{2} - 70 a + 88\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}+{y}={x}^{3}+\left(-5a^{4}-2a^{3}+38a^{2}+16a-18\right){x}^{2}+\left(-17a^{4}-8a^{3}+132a^{2}+62a-69\right){x}+20a^{4}+9a^{3}-156a^{2}-70a+88$ |
| 1.1-a3 |
1.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$37.80891$ |
$\textsf{none}$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.017072839$ |
$17159.21048$ |
0.865480808 |
\( -32384 a^{4} + 32640 a^{3} + 223360 a^{2} - 222592 a + 53504 \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -3 a^{4} - a^{3} + 23 a^{2} + 10 a - 11\) , \( -a^{4} + 7 a^{2} + a - 1\) , \( 3 a^{4} + 2 a^{3} - 21 a^{2} - 9 a + 8\) , \( 3 a^{4} + 2 a^{3} - 21 a^{2} - 9 a + 8\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(-a^{4}+7a^{2}+a-1\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+23a^{2}+10a-11\right){x}^{2}+\left(3a^{4}+2a^{3}-21a^{2}-9a+8\right){x}+3a^{4}+2a^{3}-21a^{2}-9a+8$ |
| 1.1-a4 |
1.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$37.80891$ |
$\textsf{none}$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.068291357$ |
$4289.802622$ |
0.865480808 |
\( 1414198780324 a^{4} + 3815036657888 a^{3} - 1021893446812 a^{2} - 2756727621312 a + 1048460789992 \) |
\( \bigl[3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 16\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 16 a + 14\) , \( a^{4} + a^{3} - 8 a^{2} - 7 a + 5\) , \( 16 a^{4} + 16 a^{3} - 125 a^{2} - 117 a + 73\) , \( -497 a^{4} - 266 a^{3} + 3815 a^{2} + 2050 a - 1754\bigr] \) |
${y}^2+\left(3a^{4}+2a^{3}-24a^{2}-15a+16\right){x}{y}+\left(a^{4}+a^{3}-8a^{2}-7a+5\right){y}={x}^{3}+\left(3a^{4}+2a^{3}-24a^{2}-16a+14\right){x}^{2}+\left(16a^{4}+16a^{3}-125a^{2}-117a+73\right){x}-497a^{4}-266a^{3}+3815a^{2}+2050a-1754$ |
| 3.1-a1 |
3.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.126260386$ |
$315.3795803$ |
3.96218181 |
\( \frac{115480250299881620}{9} a^{4} - \frac{306420414921106792}{9} a^{3} - \frac{110772490972874828}{9} a^{2} + \frac{293928637451461840}{9} a - \frac{87041773664501912}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -a^{4} - a^{3} + 8 a^{2} + 7 a - 6\) , \( -a^{4} + 7 a^{2} + 2 a - 1\) , \( 20 a^{4} + 15 a^{3} - 152 a^{2} - 112 a + 55\) , \( -84 a^{4} - 45 a^{3} + 652 a^{2} + 348 a - 353\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){x}{y}+\left(-a^{4}+7a^{2}+2a-1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+8a^{2}+7a-6\right){x}^{2}+\left(20a^{4}+15a^{3}-152a^{2}-112a+55\right){x}-84a^{4}-45a^{3}+652a^{2}+348a-353$ |
| 3.1-a2 |
3.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.531565096$ |
$1261.518321$ |
3.96218181 |
\( -\frac{55760981120}{9} a^{4} - \frac{31722753152}{9} a^{3} + \frac{428040546944}{9} a^{2} + \frac{243514885760}{9} a - \frac{196028708608}{9} \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -3 a^{4} - a^{3} + 23 a^{2} + 10 a - 12\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 15\) , \( 1699 a^{4} + 779 a^{3} - 13233 a^{2} - 6063 a + 7411\) , \( -13782 a^{4} - 6317 a^{3} + 107362 a^{2} + 49213 a - 60139\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-15a+15\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+23a^{2}+10a-12\right){x}^{2}+\left(1699a^{4}+779a^{3}-13233a^{2}-6063a+7411\right){x}-13782a^{4}-6317a^{3}+107362a^{2}+49213a-60139$ |
| 3.1-a3 |
3.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.063130193$ |
$2523.036642$ |
3.96218181 |
\( \frac{990434096}{81} a^{4} - \frac{2644753120}{81} a^{3} - \frac{911466176}{81} a^{2} + \frac{2557919296}{81} a - \frac{769819328}{81} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -a^{4} + 7 a^{2} - 2\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 14 a + 15\) , \( -2 a^{4} - a^{3} + 16 a^{2} + 7 a - 11\) , \( a^{4} - a^{3} - 6 a^{2} + 10 a - 7\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-14a+15\right){y}={x}^{3}+\left(-a^{4}+7a^{2}-2\right){x}^{2}+\left(-2a^{4}-a^{3}+16a^{2}+7a-11\right){x}+a^{4}-a^{3}-6a^{2}+10a-7$ |
| 3.1-a4 |
3.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.531565096$ |
$1261.518321$ |
3.96218181 |
\( \frac{8889203697164}{6561} a^{4} + \frac{24837220707752}{6561} a^{3} - \frac{5030976944660}{6561} a^{2} - \frac{19443915690704}{6561} a + \frac{7185648285352}{6561} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -a^{4} - a^{3} + 8 a^{2} + 7 a - 6\) , \( -a^{4} + 7 a^{2} + a - 1\) , \( -2 a^{4} - 10 a^{3} + 22 a^{2} + 72 a - 53\) , \( 147 a^{4} + 55 a^{3} - 1116 a^{2} - 437 a + 437\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){x}{y}+\left(-a^{4}+7a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+8a^{2}+7a-6\right){x}^{2}+\left(-2a^{4}-10a^{3}+22a^{2}+72a-53\right){x}+147a^{4}+55a^{3}-1116a^{2}-437a+437$ |
| 3.1-b1 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.177235790$ |
$1715.260606$ |
1.79624644 |
\( -\frac{109408423131008}{729} a^{4} - \frac{62238029686400}{729} a^{3} + \frac{839854325061248}{729} a^{2} + \frac{477763384026752}{729} a - \frac{384610577621248}{729} \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -5 a^{4} - 2 a^{3} + 38 a^{2} + 16 a - 18\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 15 a + 17\) , \( 28 a^{4} + 17 a^{3} - 216 a^{2} - 129 a + 100\) , \( 99 a^{4} + 58 a^{3} - 762 a^{2} - 439 a + 347\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-15a+17\right){y}={x}^{3}+\left(-5a^{4}-2a^{3}+38a^{2}+16a-18\right){x}^{2}+\left(28a^{4}+17a^{3}-216a^{2}-129a+100\right){x}+99a^{4}+58a^{3}-762a^{2}-439a+347$ |
| 3.1-b2 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.059078596$ |
$5145.781819$ |
1.79624644 |
\( -\frac{436830369580}{6561} a^{4} - \frac{279315833128}{6561} a^{3} + \frac{3417436551964}{6561} a^{2} + \frac{1973812073464}{6561} a - \frac{1576406614472}{6561} \) |
\( \bigl[5 a^{4} + 3 a^{3} - 39 a^{2} - 23 a + 22\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 7 a + 11\) , \( -3 a^{4} + 20 a^{2} + 8 a - 6\) , \( 4 a^{4} - 6 a^{3} - 21 a^{2} + 24 a - 7\bigr] \) |
${y}^2+\left(5a^{4}+3a^{3}-39a^{2}-23a+22\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-7a+11\right){y}={x}^{3}+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}^{2}+\left(-3a^{4}+20a^{2}+8a-6\right){x}+4a^{4}-6a^{3}-21a^{2}+24a-7$ |
| 3.1-b3 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.059078596$ |
$5145.781819$ |
1.79624644 |
\( -\frac{31616}{9} a^{4} + \frac{9088}{9} a^{3} + \frac{325760}{9} a^{2} + \frac{158336}{9} a - \frac{135424}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( -7 a^{4} - 4 a^{3} + 54 a^{2} + 32 a - 26\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 8 a + 11\) , \( -21 a^{4} - 12 a^{3} + 161 a^{2} + 89 a - 78\) , \( -15 a^{4} - 10 a^{3} + 110 a^{2} + 62 a - 54\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-8a+11\right){y}={x}^{3}+\left(-7a^{4}-4a^{3}+54a^{2}+32a-26\right){x}^{2}+\left(-21a^{4}-12a^{3}+161a^{2}+89a-78\right){x}-15a^{4}-10a^{3}+110a^{2}+62a-54$ |
| 3.1-b4 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.118157193$ |
$10291.56363$ |
1.79624644 |
\( -\frac{3199312}{81} a^{4} + \frac{2825696}{81} a^{3} + \frac{22241920}{81} a^{2} - \frac{19342016}{81} a + \frac{4427200}{81} \) |
\( \bigl[5 a^{4} + 3 a^{3} - 39 a^{2} - 22 a + 22\) , \( -a^{4} + 8 a^{2} - 6\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 15\) , \( -8 a^{4} - 6 a^{3} + 56 a^{2} + 30 a - 32\) , \( -a^{4} + 12 a^{2} + 10 a - 10\bigr] \) |
${y}^2+\left(5a^{4}+3a^{3}-39a^{2}-22a+22\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-15a+15\right){y}={x}^{3}+\left(-a^{4}+8a^{2}-6\right){x}^{2}+\left(-8a^{4}-6a^{3}+56a^{2}+30a-32\right){x}-a^{4}+12a^{2}+10a-10$ |
| 3.1-b5 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.354471580$ |
$3430.521212$ |
1.79624644 |
\( \frac{3690889995824}{531441} a^{4} + \frac{8511137374304}{531441} a^{3} - \frac{7153134787328}{531441} a^{2} - \frac{8065591184960}{531441} a + \frac{5179948372288}{531441} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -5 a^{4} - 2 a^{3} + 38 a^{2} + 18 a - 18\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 14 a + 15\) , \( -20 a^{4} - 11 a^{3} + 156 a^{2} + 80 a - 84\) , \( 9 a^{4} + 4 a^{3} - 71 a^{2} - 28 a + 41\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-14a+15\right){y}={x}^{3}+\left(-5a^{4}-2a^{3}+38a^{2}+18a-18\right){x}^{2}+\left(-20a^{4}-11a^{3}+156a^{2}+80a-84\right){x}+9a^{4}+4a^{3}-71a^{2}-28a+41$ |
| 3.1-b6 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.236314386$ |
$1286.445454$ |
1.79624644 |
\( -\frac{168878185588}{9} a^{4} + \frac{181111874024}{9} a^{3} + \frac{1157041071364}{9} a^{2} - \frac{1241007836984}{9} a + \frac{315878188888}{9} \) |
\( \bigl[a\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 14\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 14 a + 15\) , \( -49 a^{4} - 29 a^{3} + 375 a^{2} + 221 a - 174\) , \( -452 a^{4} - 262 a^{3} + 3474 a^{2} + 2014 a - 1611\bigr] \) |
${y}^2+a{x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-14a+15\right){y}={x}^{3}+\left(3a^{4}+2a^{3}-24a^{2}-15a+14\right){x}^{2}+\left(-49a^{4}-29a^{3}+375a^{2}+221a-174\right){x}-452a^{4}-262a^{3}+3474a^{2}+2014a-1611$ |
| 3.1-b7 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{24} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.177235790$ |
$1715.260606$ |
1.79624644 |
\( \frac{785804269820720626202012}{282429536481} a^{4} + \frac{360179462583929710200368}{282429536481} a^{3} - \frac{6121343117426130500012996}{282429536481} a^{2} - \frac{2805764946731040211400744}{282429536481} a + \frac{3428781562328144873163832}{282429536481} \) |
\( \bigl[3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 16\) , \( -2 a^{4} - a^{3} + 15 a^{2} + 8 a - 6\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 8 a + 11\) , \( 14 a^{4} + 19 a^{3} - 104 a^{2} - 136 a + 6\) , \( 222 a^{4} + 119 a^{3} - 1717 a^{2} - 918 a + 880\bigr] \) |
${y}^2+\left(3a^{4}+2a^{3}-24a^{2}-15a+16\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-8a+11\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+15a^{2}+8a-6\right){x}^{2}+\left(14a^{4}+19a^{3}-104a^{2}-136a+6\right){x}+222a^{4}+119a^{3}-1717a^{2}-918a+880$ |
| 3.1-b8 |
3.1-b |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.708943160$ |
$428.8151515$ |
1.79624644 |
\( \frac{2319368990466352580}{729} a^{4} + \frac{6256879024975420880}{729} a^{3} - \frac{1675965386577470684}{729} a^{2} - \frac{4521190866299603864}{729} a + \frac{1719535798854484696}{729} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -a^{4} + 7 a^{2} - 2\) , \( -a^{4} + 7 a^{2} + a - 1\) , \( -262 a^{4} - 120 a^{3} + 2041 a^{2} + 937 a - 1148\) , \( 643 a^{4} + 292 a^{3} - 5006 a^{2} - 2274 a + 2785\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){x}{y}+\left(-a^{4}+7a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+7a^{2}-2\right){x}^{2}+\left(-262a^{4}-120a^{3}+2041a^{2}+937a-1148\right){x}+643a^{4}+292a^{3}-5006a^{2}-2274a+2785$ |
| 3.1-c1 |
3.1-c |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.062422735$ |
$2966.040648$ |
1.09396713 |
\( -\frac{124723540192240704004}{9} a^{4} - \frac{70955992095062482480}{9} a^{3} + \frac{957421019531950412356}{9} a^{2} + \frac{544682729409745301296}{9} a - \frac{438467873361408576920}{9} \) |
\( \bigl[a\) , \( -7 a^{4} - 4 a^{3} + 54 a^{2} + 32 a - 26\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 17\) , \( -2 a^{4} + 17 a^{2} + 6 a - 7\) , \( -2 a^{4} + 18 a^{2} + 7 a - 10\bigr] \) |
${y}^2+a{x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+17\right){y}={x}^{3}+\left(-7a^{4}-4a^{3}+54a^{2}+32a-26\right){x}^{2}+\left(-2a^{4}+17a^{2}+6a-7\right){x}-2a^{4}+18a^{2}+7a-10$ |
| 3.1-c2 |
3.1-c |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.031211367$ |
$23728.32518$ |
1.09396713 |
\( -\frac{270354285904}{81} a^{4} - \frac{153806635360}{81} a^{3} + \frac{2075333050816}{81} a^{2} + \frac{1180671579328}{81} a - \frac{950432643392}{81} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -a^{4} - a^{3} + 8 a^{2} + 6 a - 5\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 17\) , \( -13 a^{4} + 13 a^{3} + 61 a^{2} + 7 a - 28\) , \( 44 a^{4} - 111 a^{3} - 55 a^{2} + 101 a - 24\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+17\right){y}={x}^{3}+\left(-a^{4}-a^{3}+8a^{2}+6a-5\right){x}^{2}+\left(-13a^{4}+13a^{3}+61a^{2}+7a-28\right){x}+44a^{4}-111a^{3}-55a^{2}+101a-24$ |
| 3.1-c3 |
3.1-c |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.015605683$ |
$11864.16259$ |
1.09396713 |
\( -\frac{162441344}{9} a^{4} + \frac{173418880}{9} a^{3} + \frac{1113649280}{9} a^{2} - \frac{1187421568}{9} a + \frac{300765440}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( 6 a^{4} + 3 a^{3} - 46 a^{2} - 24 a + 23\) , \( -a^{4} + 7 a^{2} + 2 a - 1\) , \( 89 a^{4} + 40 a^{3} - 693 a^{2} - 312 a + 390\) , \( 31368 a^{4} + 14378 a^{3} - 244354 a^{2} - 112002 a + 136868\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+\left(-a^{4}+7a^{2}+2a-1\right){y}={x}^{3}+\left(6a^{4}+3a^{3}-46a^{2}-24a+23\right){x}^{2}+\left(89a^{4}+40a^{3}-693a^{2}-312a+390\right){x}+31368a^{4}+14378a^{3}-244354a^{2}-112002a+136868$ |
| 3.1-c4 |
3.1-c |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$42.19940$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.015605683$ |
$11864.16259$ |
1.09396713 |
\( \frac{10949837991140}{6561} a^{4} + \frac{3670735225136}{6561} a^{3} - \frac{82338502777892}{6561} a^{2} - \frac{36447502271024}{6561} a + \frac{45561089776552}{6561} \) |
\( \bigl[a\) , \( -7 a^{4} - 4 a^{3} + 54 a^{2} + 32 a - 26\) , \( -2 a^{4} - a^{3} + 15 a^{2} + 9 a - 5\) , \( -18 a^{4} - 9 a^{3} + 132 a^{2} + 74 a - 61\) , \( -9 a^{4} - 10 a^{3} + 82 a^{2} + 51 a - 40\bigr] \) |
${y}^2+a{x}{y}+\left(-2a^{4}-a^{3}+15a^{2}+9a-5\right){y}={x}^{3}+\left(-7a^{4}-4a^{3}+54a^{2}+32a-26\right){x}^{2}+\left(-18a^{4}-9a^{3}+132a^{2}+74a-61\right){x}-9a^{4}-10a^{3}+82a^{2}+51a-40$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{19} \cdot 3 \) |
$45.22820$ |
$(a), (2a^4+a^3-15a^2-7a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$657.7539450$ |
1.55456123 |
\( -\frac{67373}{48} a^{4} - \frac{14263}{24} a^{3} + \frac{256813}{24} a^{2} + \frac{222041}{48} a - \frac{109283}{24} \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 7 a + 5\) , \( -7 a^{4} - 4 a^{3} + 54 a^{2} + 31 a - 26\) , \( -a^{4} + 7 a^{2} + a - 1\) , \( -23 a^{4} - 8 a^{3} + 172 a^{2} + 61 a - 62\) , \( -19 a^{4} - 15 a^{3} + 137 a^{2} + 90 a - 68\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-7a+5\right){x}{y}+\left(-a^{4}+7a^{2}+a-1\right){y}={x}^{3}+\left(-7a^{4}-4a^{3}+54a^{2}+31a-26\right){x}^{2}+\left(-23a^{4}-8a^{3}+172a^{2}+61a-62\right){x}-19a^{4}-15a^{3}+137a^{2}+90a-68$ |
| 6.1-b1 |
6.1-b |
$2$ |
$3$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$45.22820$ |
$(a), (2a^4+a^3-15a^2-7a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$303.6948165$ |
2.15329239 |
\( -\frac{11440555660285}{54} a^{4} - \frac{3740723760397}{54} a^{3} + \frac{85821348341287}{54} a^{2} + \frac{18947506759838}{27} a - \frac{23723976425302}{27} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 17\) , \( 7 a^{4} + 4 a^{3} - 54 a^{2} - 32 a + 26\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -28 a^{4} - 8 a^{3} + 213 a^{2} + 66 a - 81\) , \( 25 a^{4} - 7 a^{3} - 182 a^{2} + 43 a + 15\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+17\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){y}={x}^{3}+\left(7a^{4}+4a^{3}-54a^{2}-32a+26\right){x}^{2}+\left(-28a^{4}-8a^{3}+213a^{2}+66a-81\right){x}+25a^{4}-7a^{3}-182a^{2}+43a+15$ |
| 6.1-b2 |
6.1-b |
$2$ |
$3$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$45.22820$ |
$(a), (2a^4+a^3-15a^2-7a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$911.0844496$ |
2.15329239 |
\( \frac{1104323}{6} a^{4} + \frac{220372}{3} a^{3} - \frac{4297411}{3} a^{2} - \frac{1971904}{3} a + \frac{1744613}{3} \) |
\( \bigl[-2 a^{4} - a^{3} + 15 a^{2} + 9 a - 5\) , \( -3 a^{4} - 2 a^{3} + 23 a^{2} + 15 a - 11\) , \( 1\) , \( -132 a^{4} - 63 a^{3} + 1027 a^{2} + 488 a - 564\) , \( 525 a^{4} + 239 a^{3} - 4091 a^{2} - 1863 a + 2301\bigr] \) |
${y}^2+\left(-2a^{4}-a^{3}+15a^{2}+9a-5\right){x}{y}+{y}={x}^{3}+\left(-3a^{4}-2a^{3}+23a^{2}+15a-11\right){x}^{2}+\left(-132a^{4}-63a^{3}+1027a^{2}+488a-564\right){x}+525a^{4}+239a^{3}-4091a^{2}-1863a+2301$ |
| 6.1-c1 |
6.1-c |
$1$ |
$1$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$45.22820$ |
$(a), (2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.011153984$ |
$6326.918495$ |
1.66788713 |
\( -\frac{12400}{3} a^{4} + \frac{141065}{12} a^{3} + \frac{6814}{3} a^{2} - \frac{145709}{12} a + \frac{56809}{12} \) |
\( \bigl[-2 a^{4} - a^{3} + 15 a^{2} + 9 a - 5\) , \( -5 a^{4} - 3 a^{3} + 39 a^{2} + 22 a - 22\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 14 a + 15\) , \( -16 a^{4} - 8 a^{3} + 123 a^{2} + 63 a - 54\) , \( -17 a^{4} - 9 a^{3} + 132 a^{2} + 72 a - 64\bigr] \) |
${y}^2+\left(-2a^{4}-a^{3}+15a^{2}+9a-5\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-14a+15\right){y}={x}^{3}+\left(-5a^{4}-3a^{3}+39a^{2}+22a-22\right){x}^{2}+\left(-16a^{4}-8a^{3}+123a^{2}+63a-54\right){x}-17a^{4}-9a^{3}+132a^{2}+72a-64$ |
| 6.1-d1 |
6.1-d |
$1$ |
$1$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{10} \cdot 3^{17} \) |
$45.22820$ |
$(a), (2a^4+a^3-15a^2-7a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$63.42948230$ |
1.49911703 |
\( \frac{952181308356475836283}{258280326} a^{4} + \frac{541701826357079143471}{258280326} a^{3} - \frac{14618545906353957774425}{516560652} a^{2} - \frac{8316581039655109960523}{516560652} a + \frac{6694821392880448575967}{516560652} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 15 a + 17\) , \( 3 a^{4} + a^{3} - 23 a^{2} - 10 a + 12\) , \( 5 a^{4} + 3 a^{3} - 39 a^{2} - 22 a + 22\) , \( 158 a^{4} + 93 a^{3} - 1220 a^{2} - 726 a + 580\) , \( 820 a^{4} + 468 a^{3} - 6272 a^{2} - 3540 a + 2866\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-15a+17\right){x}{y}+\left(5a^{4}+3a^{3}-39a^{2}-22a+22\right){y}={x}^{3}+\left(3a^{4}+a^{3}-23a^{2}-10a+12\right){x}^{2}+\left(158a^{4}+93a^{3}-1220a^{2}-726a+580\right){x}+820a^{4}+468a^{3}-6272a^{2}-3540a+2866$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{8} \) |
$46.54823$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.077543161$ |
$3187.274288$ |
2.92063524 |
\( -42019352504 a^{4} - 23905075256 a^{3} + 322555084296 a^{2} + 183503634808 a - 147719748912 \) |
\( \bigl[-a^{4} + 7 a^{2} + 2 a\) , \( -a^{4} + 8 a^{2} + a - 6\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -5 a^{4} - 5 a^{3} + 31 a^{2} + 16 a - 14\) , \( 4 a^{4} + 7 a^{3} - 8 a^{2} + 8 a - 5\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+2a\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){y}={x}^{3}+\left(-a^{4}+8a^{2}+a-6\right){x}^{2}+\left(-5a^{4}-5a^{3}+31a^{2}+16a-14\right){x}+4a^{4}+7a^{3}-8a^{2}+8a-5$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$46.54823$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.155086323$ |
$12749.09715$ |
2.92063524 |
\( -229952 a^{4} - 53376 a^{3} + 1726272 a^{2} + 451328 a - 552192 \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -a^{4} + 7 a^{2}\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 16\) , \( -5 a^{4} + 38 a^{2} + 2 a - 15\) , \( -7 a^{4} - a^{3} + 53 a^{2} + 9 a - 21\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-15a+16\right){y}={x}^{3}+\left(-a^{4}+7a^{2}\right){x}^{2}+\left(-5a^{4}+38a^{2}+2a-15\right){x}-7a^{4}-a^{3}+53a^{2}+9a-21$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$46.54823$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.077543161$ |
$12749.09715$ |
2.92063524 |
\( 1107296 a^{4} + 420128 a^{3} - 8433344 a^{2} - 3782784 a + 4688128 \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( 3 a^{4} + a^{3} - 23 a^{2} - 9 a + 12\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( 5 a^{4} + a^{3} - 38 a^{2} - 10 a + 18\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 17\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){y}={x}^{3}+\left(3a^{4}+a^{3}-23a^{2}-9a+12\right){x}^{2}+\left(5a^{4}+a^{3}-38a^{2}-10a+18\right){x}+4a^{4}+2a^{3}-31a^{2}-16a+17$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$46.54823$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.310172647$ |
$796.8185721$ |
2.92063524 |
\( -33493135784 a^{4} + 35887456024 a^{3} + 229492247736 a^{2} - 245897771256 a + 62517181696 \) |
\( \bigl[-a^{4} + 7 a^{2} + 2 a\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -2 a^{4} - a^{3} + 15 a^{2} + 8 a - 6\) , \( 60 a^{4} + 27 a^{3} - 466 a^{2} - 212 a + 260\) , \( 167 a^{4} + 73 a^{3} - 1297 a^{2} - 576 a + 716\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+2a\right){x}{y}+\left(-2a^{4}-a^{3}+15a^{2}+8a-6\right){y}={x}^{3}+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){x}^{2}+\left(60a^{4}+27a^{3}-466a^{2}-212a+260\right){x}+167a^{4}+73a^{3}-1297a^{2}-576a+716$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$46.54823$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2200.686420$ |
2.60059390 |
\( 11692056768 a^{4} + 31563132928 a^{3} - 8377245248 a^{2} - 22766872448 a + 8639693312 \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 14\) , \( a\) , \( -1808 a^{4} - 828 a^{3} + 14084 a^{2} + 6451 a - 7886\) , \( 29485 a^{4} + 13515 a^{3} - 229686 a^{2} - 105280 a + 128656\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+a{y}={x}^{3}+\left(3a^{4}+2a^{3}-24a^{2}-15a+14\right){x}^{2}+\left(-1808a^{4}-828a^{3}+14084a^{2}+6451a-7886\right){x}+29485a^{4}+13515a^{3}-229686a^{2}-105280a+128656$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$46.54823$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2200.686420$ |
2.60059390 |
\( 21156631584 a^{4} + 9701675552 a^{3} - 164810941184 a^{2} - 75572643072 a + 92332939904 \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -2 a^{4} - a^{3} + 16 a^{2} + 8 a - 10\) , \( -a^{4} + 7 a^{2} + 2 a\) , \( 14 a^{4} - a^{3} - 103 a^{2} + 6 a + 18\) , \( -30 a^{4} + 10 a^{3} + 216 a^{2} - 58 a - 20\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(-a^{4}+7a^{2}+2a\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+16a^{2}+8a-10\right){x}^{2}+\left(14a^{4}-a^{3}-103a^{2}+6a+18\right){x}-30a^{4}+10a^{3}+216a^{2}-58a-20$ |
| 8.1-c1 |
8.1-c |
$2$ |
$2$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$46.54823$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.041110030$ |
$7556.224788$ |
1.83542670 |
\( -4672 a^{4} - 512 a^{3} + 35264 a^{2} + 6272 a - 9728 \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( -6 a^{4} - 3 a^{3} + 46 a^{2} + 23 a - 21\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -12 a^{4} - 6 a^{3} + 92 a^{2} + 47 a - 43\) , \( -10 a^{4} - 5 a^{3} + 77 a^{2} + 39 a - 38\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){y}={x}^{3}+\left(-6a^{4}-3a^{3}+46a^{2}+23a-21\right){x}^{2}+\left(-12a^{4}-6a^{3}+92a^{2}+47a-43\right){x}-10a^{4}-5a^{3}+77a^{2}+39a-38$ |
| 8.1-c2 |
8.1-c |
$2$ |
$2$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$46.54823$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.020555015$ |
$7556.224788$ |
1.83542670 |
\( 9248 a^{4} - 8160 a^{3} - 44288 a^{2} - 10496 a + 21376 \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -3 a^{4} - 2 a^{3} + 23 a^{2} + 14 a - 10\) , \( 5 a^{4} + 3 a^{3} - 39 a^{2} - 22 a + 22\) , \( 3 a^{4} - 19 a^{3} - 12 a^{2} + 132 a - 59\) , \( -45 a^{4} + 35 a^{3} + 316 a^{2} - 238 a + 37\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(5a^{4}+3a^{3}-39a^{2}-22a+22\right){y}={x}^{3}+\left(-3a^{4}-2a^{3}+23a^{2}+14a-10\right){x}^{2}+\left(3a^{4}-19a^{3}-12a^{2}+132a-59\right){x}-45a^{4}+35a^{3}+316a^{2}-238a+37$ |
| 8.1-d1 |
8.1-d |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$46.54823$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$230.9387350$ |
1.09161916 |
\( -33424471629018072 a^{4} - 19015388282233192 a^{3} + 256577801231801784 a^{2} + 145968695307324232 a - 117504337760259168 \) |
\( \bigl[5 a^{4} + 3 a^{3} - 39 a^{2} - 22 a + 22\) , \( -a\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( 14 a^{4} + 9 a^{3} - 105 a^{2} - 72 a + 42\) , \( 9 a^{4} + 10 a^{3} - 65 a^{2} - 74 a - 1\bigr] \) |
${y}^2+\left(5a^{4}+3a^{3}-39a^{2}-22a+22\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){y}={x}^{3}-a{x}^{2}+\left(14a^{4}+9a^{3}-105a^{2}-72a+42\right){x}+9a^{4}+10a^{3}-65a^{2}-74a-1$ |
| 8.1-d2 |
8.1-d |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$46.54823$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$3695.019760$ |
1.09161916 |
\( -163003712 a^{4} - 92757120 a^{3} + 1251121472 a^{2} + 712030464 a - 571947264 \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -3 a^{4} - 2 a^{3} + 23 a^{2} + 14 a - 11\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( 43 a^{4} + 24 a^{3} - 331 a^{2} - 189 a + 149\) , \( 206 a^{4} + 118 a^{3} - 1579 a^{2} - 901 a + 721\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){y}={x}^{3}+\left(-3a^{4}-2a^{3}+23a^{2}+14a-11\right){x}^{2}+\left(43a^{4}+24a^{3}-331a^{2}-189a+149\right){x}+206a^{4}+118a^{3}-1579a^{2}-901a+721$ |
| 8.1-d3 |
8.1-d |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$46.54823$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3695.019760$ |
1.09161916 |
\( -38941424544 a^{4} + 41725215520 a^{3} + 266823419968 a^{2} - 285897744512 a + 72686825472 \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -a^{4} + 7 a^{2} + a - 1\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -a^{4} + 3 a^{3} + 16 a^{2} - 5\) , \( 8 a^{4} + 22 a^{3} - 6 a^{2} - 19 a + 6\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){y}={x}^{3}+\left(-a^{4}+7a^{2}+a-1\right){x}^{2}+\left(-a^{4}+3a^{3}+16a^{2}-5\right){x}+8a^{4}+22a^{3}-6a^{2}-19a+6$ |
| 8.1-d4 |
8.1-d |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{8} \) |
$46.54823$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$923.7549401$ |
1.09161916 |
\( 1102832362360 a^{4} + 505491662408 a^{3} - 8590961011192 a^{2} - 3937733245640 a + 4812102100272 \) |
\( \bigl[-2 a^{4} - a^{3} + 15 a^{2} + 8 a - 6\) , \( 3 a^{4} + a^{3} - 23 a^{2} - 8 a + 11\) , \( -a^{4} + 7 a^{2} + 2 a\) , \( -198 a^{4} - 87 a^{3} + 1536 a^{2} + 696 a - 862\) , \( -1401 a^{4} - 631 a^{3} + 10889 a^{2} + 4982 a - 6100\bigr] \) |
${y}^2+\left(-2a^{4}-a^{3}+15a^{2}+8a-6\right){x}{y}+\left(-a^{4}+7a^{2}+2a\right){y}={x}^{3}+\left(3a^{4}+a^{3}-23a^{2}-8a+11\right){x}^{2}+\left(-198a^{4}-87a^{3}+1536a^{2}+696a-862\right){x}-1401a^{4}-631a^{3}+10889a^{2}+4982a-6100$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$317.8498651$ |
0.751218722 |
\( \frac{115480250299881620}{9} a^{4} - \frac{306420414921106792}{9} a^{3} - \frac{110772490972874828}{9} a^{2} + \frac{293928637451461840}{9} a - \frac{87041773664501912}{9} \) |
\( \bigl[-a^{4} + 7 a^{2} + a\) , \( -7 a^{4} - 4 a^{3} + 54 a^{2} + 31 a - 27\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 8 a + 11\) , \( 557 a^{4} + 318 a^{3} - 4276 a^{2} - 2440 a + 1958\) , \( -534 a^{4} - 299 a^{3} + 4097 a^{2} + 2298 a - 1866\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+a\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-8a+11\right){y}={x}^{3}+\left(-7a^{4}-4a^{3}+54a^{2}+31a-27\right){x}^{2}+\left(557a^{4}+318a^{3}-4276a^{2}-2440a+1958\right){x}-534a^{4}-299a^{3}+4097a^{2}+2298a-1866$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$635.6997302$ |
0.751218722 |
\( -\frac{55760981120}{9} a^{4} - \frac{31722753152}{9} a^{3} + \frac{428040546944}{9} a^{2} + \frac{243514885760}{9} a - \frac{196028708608}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( -a^{4} + 7 a^{2} - 1\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 17\) , \( 6 a^{4} + 4 a^{3} - 48 a^{2} - 30 a + 32\) , \( 13 a^{4} + 7 a^{3} - 102 a^{2} - 53 a + 60\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-16a+17\right){y}={x}^{3}+\left(-a^{4}+7a^{2}-1\right){x}^{2}+\left(6a^{4}+4a^{3}-48a^{2}-30a+32\right){x}+13a^{4}+7a^{3}-102a^{2}-53a+60$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1271.399460$ |
0.751218722 |
\( \frac{990434096}{81} a^{4} - \frac{2644753120}{81} a^{3} - \frac{911466176}{81} a^{2} + \frac{2557919296}{81} a - \frac{769819328}{81} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( -2 a^{4} - a^{3} + 16 a^{2} + 7 a - 9\) , \( 1\) , \( -7 a^{4} - 9 a^{3} + 46 a^{2} + 39 a - 34\) , \( -5 a^{4} - 16 a^{3} - 16 a^{2} - 18 a + 18\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}+{y}={x}^{3}+\left(-2a^{4}-a^{3}+16a^{2}+7a-9\right){x}^{2}+\left(-7a^{4}-9a^{3}+46a^{2}+39a-34\right){x}-5a^{4}-16a^{3}-16a^{2}-18a+18$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$317.8498651$ |
0.751218722 |
\( \frac{8889203697164}{6561} a^{4} + \frac{24837220707752}{6561} a^{3} - \frac{5030976944660}{6561} a^{2} - \frac{19443915690704}{6561} a + \frac{7185648285352}{6561} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 7 a + 10\) , \( -4 a^{4} - 2 a^{3} + 31 a^{2} + 15 a - 17\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 15\) , \( -10 a^{4} - 2 a^{3} + 70 a^{2} + 34 a - 40\) , \( -9 a^{4} + 13 a^{3} + 32 a^{2} - 2 a - 12\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-7a+10\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-15a+15\right){y}={x}^{3}+\left(-4a^{4}-2a^{3}+31a^{2}+15a-17\right){x}^{2}+\left(-10a^{4}-2a^{3}+70a^{2}+34a-40\right){x}-9a^{4}+13a^{3}+32a^{2}-2a-12$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.003631528$ |
$23167.34436$ |
1.98842902 |
\( 39422 a^{4} + 22869 a^{3} - 303012 a^{2} - 175095 a + 137083 \) |
\( \bigl[5 a^{4} + 3 a^{3} - 39 a^{2} - 23 a + 21\) , \( a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -2 a^{4} - a^{3} + 15 a^{2} + 9 a - 6\) , \( -11 a^{4} - 4 a^{3} + 84 a^{2} + 34 a - 34\) , \( a^{4} + 2 a^{3} - 8 a^{2} - 15 a + 9\bigr] \) |
${y}^2+\left(5a^{4}+3a^{3}-39a^{2}-23a+21\right){x}{y}+\left(-2a^{4}-a^{3}+15a^{2}+9a-6\right){y}={x}^{3}+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}^{2}+\left(-11a^{4}-4a^{3}+84a^{2}+34a-34\right){x}+a^{4}+2a^{3}-8a^{2}-15a+9$ |
| 9.1-c1 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$94.24539446$ |
1.00234452 |
\( -\frac{109408423131008}{729} a^{4} - \frac{62238029686400}{729} a^{3} + \frac{839854325061248}{729} a^{2} + \frac{477763384026752}{729} a - \frac{384610577621248}{729} \) |
\( \bigl[a^{4} + a^{3} - 8 a^{2} - 6 a + 6\) , \( -a^{4} + 8 a^{2} + a - 5\) , \( 4 a^{4} + 2 a^{3} - 31 a^{2} - 15 a + 17\) , \( 2 a^{4} - 13 a^{2} - 7\) , \( a^{4} - 8 a^{3} - 3 a^{2} + 53 a - 37\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-8a^{2}-6a+6\right){x}{y}+\left(4a^{4}+2a^{3}-31a^{2}-15a+17\right){y}={x}^{3}+\left(-a^{4}+8a^{2}+a-5\right){x}^{2}+\left(2a^{4}-13a^{2}-7\right){x}+a^{4}-8a^{3}-3a^{2}+53a-37$ |
| 9.1-c2 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3816.938475$ |
1.00234452 |
\( -\frac{436830369580}{6561} a^{4} - \frac{279315833128}{6561} a^{3} + \frac{3417436551964}{6561} a^{2} + \frac{1973812073464}{6561} a - \frac{1576406614472}{6561} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 15 a + 16\) , \( -3 a^{4} - 2 a^{3} + 24 a^{2} + 14 a - 15\) , \( a^{4} + a^{3} - 8 a^{2} - 7 a + 5\) , \( -4 a^{4} + 33 a^{2} + 9 a - 17\) , \( -2 a^{4} - 2 a^{3} + 14 a^{2} + 10 a - 10\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-15a+16\right){x}{y}+\left(a^{4}+a^{3}-8a^{2}-7a+5\right){y}={x}^{3}+\left(-3a^{4}-2a^{3}+24a^{2}+14a-15\right){x}^{2}+\left(-4a^{4}+33a^{2}+9a-17\right){x}-2a^{4}-2a^{3}+14a^{2}+10a-10$ |
| 9.1-c3 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7633.876951$ |
1.00234452 |
\( -\frac{31616}{9} a^{4} + \frac{9088}{9} a^{3} + \frac{325760}{9} a^{2} + \frac{158336}{9} a - \frac{135424}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 16 a^{2} - 8 a + 10\) , \( 6 a^{4} + 3 a^{3} - 46 a^{2} - 25 a + 22\) , \( -2 a^{4} - a^{3} + 15 a^{2} + 8 a - 5\) , \( -5 a^{4} - 5 a^{3} + 39 a^{2} + 33 a - 20\) , \( 11 a^{4} + 6 a^{3} - 82 a^{2} - 44 a + 38\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-16a^{2}-8a+10\right){x}{y}+\left(-2a^{4}-a^{3}+15a^{2}+8a-5\right){y}={x}^{3}+\left(6a^{4}+3a^{3}-46a^{2}-25a+22\right){x}^{2}+\left(-5a^{4}-5a^{3}+39a^{2}+33a-20\right){x}+11a^{4}+6a^{3}-82a^{2}-44a+38$ |
| 9.1-c4 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$15267.75390$ |
1.00234452 |
\( -\frac{3199312}{81} a^{4} + \frac{2825696}{81} a^{3} + \frac{22241920}{81} a^{2} - \frac{19342016}{81} a + \frac{4427200}{81} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 16 a + 16\) , \( a^{4} + a^{3} - 8 a^{2} - 7 a + 6\) , \( -a^{4} + 7 a^{2} + 2 a - 1\) , \( 23 a^{4} + 14 a^{3} - 176 a^{2} - 107 a + 80\) , \( -50 a^{4} - 28 a^{3} + 383 a^{2} + 217 a - 176\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-16a+16\right){x}{y}+\left(-a^{4}+7a^{2}+2a-1\right){y}={x}^{3}+\left(a^{4}+a^{3}-8a^{2}-7a+6\right){x}^{2}+\left(23a^{4}+14a^{3}-176a^{2}-107a+80\right){x}-50a^{4}-28a^{3}+383a^{2}+217a-176$ |
| 9.1-c5 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$188.4907889$ |
1.00234452 |
\( \frac{3690889995824}{531441} a^{4} + \frac{8511137374304}{531441} a^{3} - \frac{7153134787328}{531441} a^{2} - \frac{8065591184960}{531441} a + \frac{5179948372288}{531441} \) |
\( \bigl[5 a^{4} + 3 a^{3} - 39 a^{2} - 22 a + 22\) , \( 3 a^{4} + 2 a^{3} - 23 a^{2} - 15 a + 11\) , \( 3 a^{4} + 2 a^{3} - 24 a^{2} - 15 a + 15\) , \( -a^{4} - 3 a^{3} - 12 a^{2} - 4 a + 3\) , \( -16 a^{4} - 33 a^{3} + 5 a^{2} + 27 a - 10\bigr] \) |
${y}^2+\left(5a^{4}+3a^{3}-39a^{2}-22a+22\right){x}{y}+\left(3a^{4}+2a^{3}-24a^{2}-15a+15\right){y}={x}^{3}+\left(3a^{4}+2a^{3}-23a^{2}-15a+11\right){x}^{2}+\left(-a^{4}-3a^{3}-12a^{2}-4a+3\right){x}-16a^{4}-33a^{3}+5a^{2}+27a-10$ |
| 9.1-c6 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3816.938475$ |
1.00234452 |
\( -\frac{168878185588}{9} a^{4} + \frac{181111874024}{9} a^{3} + \frac{1157041071364}{9} a^{2} - \frac{1241007836984}{9} a + \frac{315878188888}{9} \) |
\( \bigl[4 a^{4} + 2 a^{3} - 31 a^{2} - 15 a + 16\) , \( -3 a^{4} - 2 a^{3} + 24 a^{2} + 14 a - 15\) , \( 5 a^{4} + 3 a^{3} - 39 a^{2} - 22 a + 21\) , \( -19 a^{4} - 11 a^{3} + 140 a^{2} + 62 a - 79\) , \( 31 a^{4} + 4 a^{3} - 275 a^{2} - 120 a + 151\bigr] \) |
${y}^2+\left(4a^{4}+2a^{3}-31a^{2}-15a+16\right){x}{y}+\left(5a^{4}+3a^{3}-39a^{2}-22a+21\right){y}={x}^{3}+\left(-3a^{4}-2a^{3}+24a^{2}+14a-15\right){x}^{2}+\left(-19a^{4}-11a^{3}+140a^{2}+62a-79\right){x}+31a^{4}+4a^{3}-275a^{2}-120a+151$ |
| 9.1-c7 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{30} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$47.12269723$ |
1.00234452 |
\( \frac{785804269820720626202012}{282429536481} a^{4} + \frac{360179462583929710200368}{282429536481} a^{3} - \frac{6121343117426130500012996}{282429536481} a^{2} - \frac{2805764946731040211400744}{282429536481} a + \frac{3428781562328144873163832}{282429536481} \) |
\( \bigl[-a^{4} + 7 a^{2} + a\) , \( -3 a^{4} - a^{3} + 23 a^{2} + 10 a - 12\) , \( -2 a^{4} - a^{3} + 15 a^{2} + 9 a - 5\) , \( 50 a^{4} + 34 a^{3} - 383 a^{2} - 258 a + 168\) , \( 63 a^{4} + 42 a^{3} - 483 a^{2} - 320 a + 209\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+a\right){x}{y}+\left(-2a^{4}-a^{3}+15a^{2}+9a-5\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+23a^{2}+10a-12\right){x}^{2}+\left(50a^{4}+34a^{3}-383a^{2}-258a+168\right){x}+63a^{4}+42a^{3}-483a^{2}-320a+209$ |
| 9.1-c8 |
9.1-c |
$8$ |
$12$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$47.09973$ |
$(2a^4+a^3-15a^2-7a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$47.12269723$ |
1.00234452 |
\( \frac{2319368990466352580}{729} a^{4} + \frac{6256879024975420880}{729} a^{3} - \frac{1675965386577470684}{729} a^{2} - \frac{4521190866299603864}{729} a + \frac{1719535798854484696}{729} \) |
\( \bigl[-a^{4} + 7 a^{2} + a\) , \( -3 a^{4} - a^{3} + 23 a^{2} + 10 a - 12\) , \( a^{4} + a^{3} - 8 a^{2} - 6 a + 5\) , \( 28 a^{4} + 16 a^{3} - 221 a^{2} - 130 a + 102\) , \( 295 a^{4} + 162 a^{3} - 2286 a^{2} - 1296 a + 1046\bigr] \) |
${y}^2+\left(-a^{4}+7a^{2}+a\right){x}{y}+\left(a^{4}+a^{3}-8a^{2}-6a+5\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+23a^{2}+10a-12\right){x}^{2}+\left(28a^{4}+16a^{3}-221a^{2}-130a+102\right){x}+295a^{4}+162a^{3}-2286a^{2}-1296a+1046$ |
*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.
