| 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 |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$41.76801110$ |
0.995405 |
\( 4004074999723542316041024 a^{5} - 1949556584033950134655008 a^{4} - 25024780887398825534345696 a^{3} + 15188137846148899288388608 a^{2} + 23809437966364673700849632 a - 7803588656580513299554352 \) |
\( \bigl[-2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 13 a + 8\) , \( 4 a^{5} - 2 a^{4} - 25 a^{3} + 17 a^{2} + 24 a - 12\) , \( -a^{5} + a^{4} + 7 a^{3} - 6 a^{2} - 7 a + 3\) , \( 8 a^{5} + 22 a^{4} - 27 a^{3} - 103 a^{2} - 13 a + 11\) , \( 1276 a^{5} + 594 a^{4} - 6840 a^{3} - 1131 a^{2} + 3731 a - 840\bigr] \) |
${y}^2+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-13a+8\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-6a^{2}-7a+3\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-25a^{3}+17a^{2}+24a-12\right){x}^{2}+\left(8a^{5}+22a^{4}-27a^{3}-103a^{2}-13a+11\right){x}+1276a^{5}+594a^{4}-6840a^{3}-1131a^{2}+3731a-840$ |
| 1.1-a2 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$41.76801110$ |
0.995405 |
\( 225028107631749153805952 a^{5} + 237143356065401540232416 a^{4} - 863114414511267120318624 a^{3} - 197501139703088449488992 a^{2} + 494476922238372675545664 a - 109564638238910304234960 \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 6 a\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( -a^{5} + a^{4} + 7 a^{3} - 7 a^{2} - 8 a + 6\) , \( -22 a^{5} + 69 a^{4} + 74 a^{3} - 373 a^{2} + 276 a - 60\) , \( -244 a^{5} + 520 a^{4} + 1081 a^{3} - 3138 a^{2} + 1871 a - 308\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+6a\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-7a^{2}-8a+6\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-4\right){x}^{2}+\left(-22a^{5}+69a^{4}+74a^{3}-373a^{2}+276a-60\right){x}-244a^{5}+520a^{4}+1081a^{3}-3138a^{2}+1871a-308$ |
| 1.1-a3 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$167.0720444$ |
0.995405 |
\( 2007702216704 a^{5} - 1003851108352 a^{4} - 12046213300224 a^{3} + 8030808866816 a^{2} + 10038511083520 a - 3394990190592 \) |
\( \bigl[0\) , \( 5 a^{5} - 2 a^{4} - 31 a^{3} + 17 a^{2} + 30 a - 10\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 3\) , \( 76 a^{5} - 90 a^{4} - 520 a^{3} + 513 a^{2} + 492 a - 312\) , \( 208 a^{5} - 479 a^{4} - 1732 a^{3} + 2217 a^{2} + 1769 a - 1253\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+3\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-31a^{3}+17a^{2}+30a-10\right){x}^{2}+\left(76a^{5}-90a^{4}-520a^{3}+513a^{2}+492a-312\right){x}+208a^{5}-479a^{4}-1732a^{3}+2217a^{2}+1769a-1253$ |
| 1.1-a4 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$30448.88009$ |
0.995405 |
\( 133398464 a^{5} - 56844192 a^{4} - 856661600 a^{3} + 509115840 a^{2} + 816668320 a - 266718192 \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 18 a + 9\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 9 a^{2} - 10 a + 6\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 7\) , \( 3 a^{5} - 3 a^{4} - 19 a^{3} + 20 a^{2} + 16 a - 14\) , \( 20 a^{5} - 13 a^{4} - 122 a^{3} + 101 a^{2} + 107 a - 68\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-18a+9\right){x}{y}+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+7\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+12a^{3}-9a^{2}-10a+6\right){x}^{2}+\left(3a^{5}-3a^{4}-19a^{3}+20a^{2}+16a-14\right){x}+20a^{5}-13a^{4}-122a^{3}+101a^{2}+107a-68$ |
| 1.1-a5 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$121795.5203$ |
0.995405 |
\( -8192 a^{5} + 4096 a^{4} + 49152 a^{3} - 32768 a^{2} - 40960 a + 36864 \) |
\( \bigl[0\) , \( 5 a^{5} - 2 a^{4} - 31 a^{3} + 17 a^{2} + 30 a - 10\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 3\) , \( 16 a^{5} - 10 a^{4} - 100 a^{3} + 73 a^{2} + 92 a - 42\) , \( -5 a^{5} + 4 a^{4} + 29 a^{3} - 31 a^{2} - 22 a + 22\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+3\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-31a^{3}+17a^{2}+30a-10\right){x}^{2}+\left(16a^{5}-10a^{4}-100a^{3}+73a^{2}+92a-42\right){x}-5a^{5}+4a^{4}+29a^{3}-31a^{2}-22a+22$ |
| 1.1-a6 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$30448.88009$ |
0.995405 |
\( -76169024 a^{5} - 54935680 a^{4} + 422361920 a^{3} + 162522016 a^{2} - 318217120 a + 69955792 \) |
\( \bigl[a^{5} - 6 a^{3} + 2 a^{2} + 7 a - 1\) , \( a^{5} - a^{4} - 6 a^{3} + 6 a^{2} + 5 a - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 5 a + 1\) , \( -7 a^{5} + 5 a^{4} + 48 a^{3} - 30 a^{2} - 49 a + 15\) , \( 2 a^{5} + 2 a^{4} - 8 a^{3} - a^{2} + 5 a - 2\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+2a^{2}+7a-1\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+6a^{2}+5a-2\right){x}^{2}+\left(-7a^{5}+5a^{4}+48a^{3}-30a^{2}-49a+15\right){x}+2a^{5}+2a^{4}-8a^{3}-a^{2}+5a-2$ |
| 1.1-a7 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$30448.88009$ |
0.995405 |
\( -347029632 a^{5} + 256679968 a^{4} + 2173100832 a^{3} - 1830838624 a^{2} - 1947452160 a + 1182258160 \) |
\( \bigl[-2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 13 a + 8\) , \( a^{5} - a^{4} - 7 a^{3} + 7 a^{2} + 9 a - 6\) , \( a^{5} - 6 a^{3} + 2 a^{2} + 6 a - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 6 a - 1\) , \( 6 a^{5} - 31 a^{3} + 8 a^{2} + 7 a - 2\bigr] \) |
${y}^2+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-13a+8\right){x}{y}+\left(a^{5}-6a^{3}+2a^{2}+6a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-7a^{3}+7a^{2}+9a-6\right){x}^{2}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+6a-1\right){x}+6a^{5}-31a^{3}+8a^{2}+7a-2$ |
| 1.1-a8 |
1.1-a |
$8$ |
$12$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$41.76801110$ |
0.995405 |
\( 277545086289159134406208 a^{5} - 540910868853676707704000 a^{4} - 1151993859956610970854784 a^{3} + 3035956068131991578113120 a^{2} - 1770673920380793355129376 a + 292487787035835453900496 \) |
\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 8 a^{2} - 13 a + 5\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 9 a^{2} + 15 a - 6\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 3\) , \( -21 a^{5} + 95 a^{4} + 73 a^{3} - 492 a^{2} + 283 a - 50\) , \( -386 a^{5} + 738 a^{4} + 1622 a^{3} - 4148 a^{2} + 2374 a - 448\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-8a^{2}-13a+5\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-3a+3\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+9a^{2}+15a-6\right){x}^{2}+\left(-21a^{5}+95a^{4}+73a^{3}-492a^{2}+283a-50\right){x}-386a^{5}+738a^{4}+1622a^{3}-4148a^{2}+2374a-448$ |
| 1.1-b1 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.813834903$ |
0.574910 |
\( 398625126729270617999810720800 a^{5} - 194087833128963095331373137056 a^{4} - 2491338562166234387363921405344 a^{3} + 1512052939605058320377241046240 a^{2} + 2370345267600799520062939441120 a - 776885177574141699802585000112 \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 6 a\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 20 a + 9\) , \( a^{5} - 6 a^{3} + 2 a^{2} + 6 a - 2\) , \( -151 a^{5} - 210 a^{4} + 718 a^{3} + 653 a^{2} - 722 a - 633\) , \( -1393 a^{5} - 3625 a^{4} + 4550 a^{3} + 12273 a^{2} - 4029 a - 9200\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+6a\right){x}{y}+\left(a^{5}-6a^{3}+2a^{2}+6a-2\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-20a+9\right){x}^{2}+\left(-151a^{5}-210a^{4}+718a^{3}+653a^{2}-722a-633\right){x}-1393a^{5}-3625a^{4}+4550a^{3}+12273a^{2}-4029a-9200$ |
| 1.1-b2 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.813834903$ |
0.574910 |
\( 22402641790849115273543877024 a^{5} + 23608773654883490938523595840 a^{4} - 85927234852474881887014678496 a^{3} - 19662198347841150992540617472 a^{2} + 49227580853717731449189062816 a - 10907692240108153801174975568 \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 5 a + 4\) , \( -a^{3} - a^{2} + 2 a\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 3\) , \( 133 a^{5} + 161 a^{4} - 1064 a^{3} - 640 a^{2} + 2071 a - 795\) , \( -124 a^{5} + 4194 a^{4} - 3721 a^{3} - 21123 a^{2} + 25536 a - 7391\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-7a^{2}-5a+4\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+2a\right){x}^{2}+\left(133a^{5}+161a^{4}-1064a^{3}-640a^{2}+2071a-795\right){x}-124a^{5}+4194a^{4}-3721a^{3}-21123a^{2}+25536a-7391$ |
| 1.1-b3 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
✓ |
$2, 7$ |
2Cs, 7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$3.255339613$ |
0.574910 |
\( 633473868775424 a^{5} - 316736934387712 a^{4} - 3800843212652544 a^{3} + 2533895475101696 a^{2} + 3167369343877120 a - 1071190523412480 \) |
\( \bigl[0\) , \( -2 a^{5} + 11 a^{3} - 3 a^{2} - 7 a + 2\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 8\) , \( 281 a^{5} - 163 a^{4} - 1787 a^{3} + 1106 a^{2} + 2260 a - 1278\) , \( 2754 a^{5} - 1515 a^{4} - 16949 a^{3} + 8607 a^{2} + 23877 a - 12426\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+8\right){y}={x}^{3}+\left(-2a^{5}+11a^{3}-3a^{2}-7a+2\right){x}^{2}+\left(281a^{5}-163a^{4}-1787a^{3}+1106a^{2}+2260a-1278\right){x}+2754a^{5}-1515a^{4}-16949a^{3}+8607a^{2}+23877a-12426$ |
| 1.1-b4 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$95746.86256$ |
0.574910 |
\( -566566560 a^{5} + 1895308960 a^{4} - 1044343008 a^{3} - 1521866464 a^{2} + 1309583520 a - 241406576 \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( -a^{4} + 5 a^{2} - 1\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 10 a + 5\) , \( 6 a^{5} - 5 a^{4} - 35 a^{3} + 41 a^{2} + 30 a - 26\) , \( -52 a^{5} + 38 a^{4} + 328 a^{3} - 267 a^{2} - 296 a + 170\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-2a+4\right){x}{y}+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-10a+5\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-1\right){x}^{2}+\left(6a^{5}-5a^{4}-35a^{3}+41a^{2}+30a-26\right){x}-52a^{5}+38a^{4}+328a^{3}-267a^{2}-296a+170$ |
| 1.1-b5 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
✓ |
$2, 7$ |
2Cs, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$382987.4502$ |
0.574910 |
\( -278528 a^{5} + 139264 a^{4} + 1671168 a^{3} - 1114112 a^{2} - 1392640 a + 786432 \) |
\( \bigl[0\) , \( 3 a^{5} - 2 a^{4} - 19 a^{3} + 14 a^{2} + 18 a - 8\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 8\) , \( a^{4} - a^{3} - 5 a^{2} + 7 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 7 a + 1\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+8\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-19a^{3}+14a^{2}+18a-8\right){x}^{2}+\left(a^{4}-a^{3}-5a^{2}+7a-1\right){x}-a^{4}+a^{3}+5a^{2}-7a+1$ |
| 1.1-b6 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$95746.86256$ |
0.574910 |
\( -17113792960 a^{5} - 7301553888 a^{4} + 92266203904 a^{3} + 11835234144 a^{2} - 51570543104 a + 11995773072 \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 18 a + 9\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 9 a^{2} - 11 a + 6\) , \( a + 1\) , \( 2 a^{5} - 4 a^{4} - 16 a^{3} + 19 a^{2} + 17 a - 10\) , \( 14 a^{5} + 5 a^{4} - 67 a^{3} + 21 a^{2} + 49 a - 23\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-18a+9\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+12a^{3}-9a^{2}-11a+6\right){x}^{2}+\left(2a^{5}-4a^{4}-16a^{3}+19a^{2}+17a-10\right){x}+14a^{5}+5a^{4}-67a^{3}+21a^{2}+49a-23$ |
| 1.1-b7 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$95746.86256$ |
0.574910 |
\( -70891544480 a^{5} + 49692196928 a^{4} + 440209563104 a^{3} - 364600983680 a^{2} - 392598560416 a + 237056103088 \) |
\( \bigl[-2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 13 a + 8\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 19 a + 9\) , \( -2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 12 a + 7\) , \( -11 a^{5} - 10 a^{4} + 44 a^{3} + 3 a^{2} - 28 a + 9\) , \( -51 a^{5} - 54 a^{4} + 195 a^{3} + 45 a^{2} - 111 a + 25\bigr] \) |
${y}^2+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-13a+8\right){x}{y}+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-12a+7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-19a+9\right){x}^{2}+\left(-11a^{5}-10a^{4}+44a^{3}+3a^{2}-28a+9\right){x}-51a^{5}-54a^{4}+195a^{3}+45a^{2}-111a+25$ |
| 1.1-b8 |
1.1-b |
$8$ |
$28$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$75.92891$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.813834903$ |
0.574910 |
\( 27630962251451422897488497216 a^{5} - 53850305911705973692572006304 a^{4} - 114686587610717667774122486400 a^{3} + 302244181829067455298671951392 a^{2} - 176279194596661470657913028736 a + 29118580763356895380422354384 \) |
\( \bigl[-2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 9 a + 4\) , \( 2 a^{5} - 12 a^{3} + 3 a^{2} + 10 a - 3\) , \( a^{5} - 6 a^{3} + a^{2} + 5 a + 1\) , \( -1888 a^{5} + 1002 a^{4} + 11783 a^{3} - 7633 a^{2} - 10880 a + 3600\) , \( -37219 a^{5} + 18799 a^{4} + 232283 a^{3} - 145308 a^{2} - 216856 a + 71547\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-9a+4\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+5a+1\right){y}={x}^{3}+\left(2a^{5}-12a^{3}+3a^{2}+10a-3\right){x}^{2}+\left(-1888a^{5}+1002a^{4}+11783a^{3}-7633a^{2}-10880a+3600\right){x}-37219a^{5}+18799a^{4}+232283a^{3}-145308a^{2}-216856a+71547$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{42} \) |
$85.22732$ |
$(2a^5-a^4-12a^3+8a^2+9a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$837.5962578$ |
0.985748 |
\( \frac{64655}{64} a^{5} - \frac{64655}{128} a^{4} - \frac{193965}{32} a^{3} + \frac{64655}{16} a^{2} + \frac{323275}{64} a - \frac{308181}{128} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 3\) , \( -a^{5} + 7 a^{3} - a^{2} - 9 a\) , \( a^{4} - 5 a^{2} + a + 3\) , \( 19 a^{5} + 2 a^{4} - 106 a^{3} + 19 a^{2} + 69 a - 21\) , \( 80 a^{5} + 34 a^{4} - 428 a^{3} - 53 a^{2} + 229 a - 55\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+3\right){x}{y}+\left(a^{4}-5a^{2}+a+3\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-a^{2}-9a\right){x}^{2}+\left(19a^{5}+2a^{4}-106a^{3}+19a^{2}+69a-21\right){x}+80a^{5}+34a^{4}-428a^{3}-53a^{2}+229a-55$ |
| 19.1-a1 |
19.1-a |
$2$ |
$2$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{6} \) |
$97.04428$ |
$(2a^5-a^4-12a^3+9a^2+11a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1040.362690$ |
0.612190 |
\( \frac{79159072}{361} a^{5} - \frac{39579536}{361} a^{4} - \frac{474954432}{361} a^{3} + \frac{316636288}{361} a^{2} + \frac{395795360}{361} a - \frac{7047424}{19} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 4 a + 3\) , \( -2 a^{5} + 11 a^{3} - 3 a^{2} - 7 a\) , \( 2 a^{5} - 12 a^{3} + 3 a^{2} + 12 a - 1\) , \( -3 a^{5} + 5 a^{4} + 11 a^{3} - 29 a^{2} + 24 a - 6\) , \( -9 a^{5} + 14 a^{4} + 42 a^{3} - 82 a^{2} + 28 a - 4\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-4a+3\right){x}{y}+\left(2a^{5}-12a^{3}+3a^{2}+12a-1\right){y}={x}^{3}+\left(-2a^{5}+11a^{3}-3a^{2}-7a\right){x}^{2}+\left(-3a^{5}+5a^{4}+11a^{3}-29a^{2}+24a-6\right){x}-9a^{5}+14a^{4}+42a^{3}-82a^{2}+28a-4$ |
| 19.1-a2 |
19.1-a |
$2$ |
$2$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$97.04428$ |
$(2a^5-a^4-12a^3+9a^2+11a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2080.725381$ |
0.612190 |
\( -\frac{5962240}{19} a^{5} + \frac{2981120}{19} a^{4} + \frac{35773440}{19} a^{3} - \frac{23848960}{19} a^{2} - \frac{29811200}{19} a + 881408 \) |
\( \bigl[a^{4} - 5 a^{2} + 2 a + 3\) , \( 3 a^{5} - a^{4} - 19 a^{3} + 9 a^{2} + 18 a - 6\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 2\) , \( 7 a^{5} - 6 a^{4} - 48 a^{3} + 37 a^{2} + 51 a - 21\) , \( -a^{5} - 12 a^{4} - 13 a^{3} + 36 a^{2} + 24 a - 16\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2a+3\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+2\right){y}={x}^{3}+\left(3a^{5}-a^{4}-19a^{3}+9a^{2}+18a-6\right){x}^{2}+\left(7a^{5}-6a^{4}-48a^{3}+37a^{2}+51a-21\right){x}-a^{5}-12a^{4}-13a^{3}+36a^{2}+24a-16$ |
| 29.1-a1 |
29.1-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.062772949$ |
$20241.56961$ |
2.24305 |
\( \frac{21219722714528}{29} a^{5} - \frac{10331737055264}{29} a^{4} - 4573090398080 a^{3} + \frac{80490018765376}{29} a^{2} + \frac{126178872734592}{29} a - \frac{41355364299504}{29} \) |
\( \bigl[a^{5} - 6 a^{3} + 2 a^{2} + 7 a - 1\) , \( a^{4} - 5 a^{2} + a + 1\) , \( a^{4} - 5 a^{2} + a + 2\) , \( 2 a^{5} - 10 a^{3} + 8 a^{2} + 9 a - 7\) , \( 5 a^{5} - 26 a^{3} + 12 a^{2} + 21 a - 11\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+2a^{2}+7a-1\right){x}{y}+\left(a^{4}-5a^{2}+a+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+a+1\right){x}^{2}+\left(2a^{5}-10a^{3}+8a^{2}+9a-7\right){x}+5a^{5}-26a^{3}+12a^{2}+21a-11$ |
| 29.1-a2 |
29.1-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.031386474$ |
$80966.27847$ |
2.24305 |
\( \frac{639930368}{841} a^{5} - \frac{311574528}{841} a^{4} - \frac{137945088}{29} a^{3} + \frac{2428588032}{841} a^{2} + \frac{3806736384}{841} a - \frac{1245786112}{841} \) |
\( \bigl[0\) , \( -a^{5} + 5 a^{3} - 2 a^{2} - 3 a + 1\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 19 a + 9\) , \( -5 a^{5} + 11 a^{4} + 22 a^{3} - 59 a^{2} + 32 a - 5\) , \( 12 a^{5} - 24 a^{4} - 51 a^{3} + 132 a^{2} - 73 a + 10\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-19a+9\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(-5a^{5}+11a^{4}+22a^{3}-59a^{2}+32a-5\right){x}+12a^{5}-24a^{4}-51a^{3}+132a^{2}-73a+10$ |
| 29.1-a3 |
29.1-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.062772949$ |
$20241.56961$ |
2.24305 |
\( -\frac{107164832}{29} a^{5} + \frac{182462464}{29} a^{4} + 4559424 a^{3} - \frac{105085248}{29} a^{2} - \frac{17471968}{29} a + \frac{9921552}{29} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 5 a + 4\) , \( a^{5} - a^{4} - 7 a^{3} + 6 a^{2} + 8 a - 3\) , \( -a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 4 a + 5\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 12 a^{2} - 8 a + 6\) , \( 2 a^{5} + 3 a^{4} - 9 a^{3} - 12 a^{2} + a + 3\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-7a^{2}-5a+4\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-7a^{2}-4a+5\right){y}={x}^{3}+\left(a^{5}-a^{4}-7a^{3}+6a^{2}+8a-3\right){x}^{2}+\left(-a^{5}+2a^{4}+7a^{3}-12a^{2}-8a+6\right){x}+2a^{5}+3a^{4}-9a^{3}-12a^{2}+a+3$ |
| 29.1-a4 |
29.1-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.015693237$ |
$20241.56961$ |
2.24305 |
\( -\frac{958436904192}{707281} a^{5} + \frac{692157350048}{707281} a^{4} + \frac{206165045824}{24389} a^{3} - \frac{4999257572608}{707281} a^{2} - \frac{5346258241568}{707281} a + \frac{3239213392944}{707281} \) |
\( \bigl[-2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 9 a + 4\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 8 a^{2} + 11 a - 3\) , \( a^{5} - 6 a^{3} + 2 a^{2} + 6 a - 2\) , \( 7 a^{5} - 5 a^{4} - 43 a^{3} + 35 a^{2} + 39 a - 19\) , \( -2 a^{5} + a^{4} + 11 a^{3} - 8 a^{2} - 10 a + 7\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-9a+4\right){x}{y}+\left(a^{5}-6a^{3}+2a^{2}+6a-2\right){y}={x}^{3}+\left(2a^{5}-a^{4}-12a^{3}+8a^{2}+11a-3\right){x}^{2}+\left(7a^{5}-5a^{4}-43a^{3}+35a^{2}+39a-19\right){x}-2a^{5}+a^{4}+11a^{3}-8a^{2}-10a+7$ |
| 29.1-b1 |
29.1-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.005398379$ |
$54056.33314$ |
2.06059 |
\( \frac{1000922698144}{707281} a^{5} - \frac{99391444864}{707281} a^{4} - \frac{194769921216}{24389} a^{3} + \frac{2619640614144}{707281} a^{2} + \frac{5009272343648}{707281} a - \frac{1580912356016}{707281} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( -3 a^{5} + a^{4} + 19 a^{3} - 10 a^{2} - 20 a + 7\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 7\) , \( -6 a^{5} - 6 a^{4} + 30 a^{3} + 21 a^{2} - 12 a + 2\) , \( -360 a^{5} - 153 a^{4} + 1944 a^{3} + 246 a^{2} - 1099 a + 257\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-2a+4\right){x}{y}+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+7\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+19a^{3}-10a^{2}-20a+7\right){x}^{2}+\left(-6a^{5}-6a^{4}+30a^{3}+21a^{2}-12a+2\right){x}-360a^{5}-153a^{4}+1944a^{3}+246a^{2}-1099a+257$ |
| 29.1-b2 |
29.1-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.010796758$ |
$216225.3325$ |
2.06059 |
\( -\frac{20250624}{841} a^{5} + \frac{8368128}{841} a^{4} + \frac{4280320}{29} a^{3} - \frac{66207744}{841} a^{2} - \frac{132702208}{841} a + \frac{70647808}{841} \) |
\( \bigl[0\) , \( 3 a^{5} - a^{4} - 18 a^{3} + 9 a^{2} + 16 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 3\) , \( -2 a^{5} + 3 a^{4} + 14 a^{3} - 17 a^{2} - 17 a + 6\) , \( -8 a^{5} - a^{4} + 45 a^{3} - 7 a^{2} - 31 a + 8\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+3\right){y}={x}^{3}+\left(3a^{5}-a^{4}-18a^{3}+9a^{2}+16a-5\right){x}^{2}+\left(-2a^{5}+3a^{4}+14a^{3}-17a^{2}-17a+6\right){x}-8a^{5}-a^{4}+45a^{3}-7a^{2}-31a+8$ |
| 29.1-b3 |
29.1-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.021593516$ |
$54056.33314$ |
2.06059 |
\( -\frac{5769573312}{29} a^{5} + \frac{7101142176}{29} a^{4} + 440434048 a^{3} - \frac{4597870976}{29} a^{2} - \frac{3870683168}{29} a + \frac{1184169008}{29} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 6 a\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 18 a + 10\) , \( -a^{5} + a^{4} + 7 a^{3} - 7 a^{2} - 8 a + 6\) , \( 8 a^{5} - 3 a^{4} - 50 a^{3} + 24 a^{2} + 49 a - 9\) , \( -14 a^{5} + 13 a^{4} + 86 a^{3} - 92 a^{2} - 70 a + 66\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+6a\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-7a^{2}-8a+6\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-18a+10\right){x}^{2}+\left(8a^{5}-3a^{4}-50a^{3}+24a^{2}+49a-9\right){x}-14a^{5}+13a^{4}+86a^{3}-92a^{2}-70a+66$ |
| 29.1-b4 |
29.1-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.021593516$ |
$54056.33314$ |
2.06059 |
\( -\frac{16342065504}{29} a^{5} + \frac{3647380704}{29} a^{4} + 3943432256 a^{3} - \frac{47788701568}{29} a^{2} - \frac{165064147136}{29} a + \frac{82158995024}{29} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 4 a + 3\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 8 a^{2} + 14 a - 6\) , \( a^{5} - 6 a^{3} + a^{2} + 5 a + 1\) , \( a^{2} + a - 3\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 8 a^{2} - 25 a + 7\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-4a+3\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+5a+1\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+8a^{2}+14a-6\right){x}^{2}+\left(a^{2}+a-3\right){x}-3a^{5}+a^{4}+20a^{3}-8a^{2}-25a+7$ |
| 29.1-c1 |
29.1-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2884.602099$ |
1.69741 |
\( -\frac{39507574489430976}{841} a^{5} + \frac{132104241463568256}{841} a^{4} - \frac{2502609667936000}{29} a^{3} - \frac{106454663882161056}{841} a^{2} + \frac{91475265749834272}{841} a - \frac{16856715142953520}{841} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 4 a + 3\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 7\) , \( -21 a^{5} - 13 a^{4} + 94 a^{3} - 11 a^{2} - 70 a + 25\) , \( -419 a^{5} - 471 a^{4} + 1566 a^{3} + 469 a^{2} - 861 a + 154\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-4a+3\right){x}{y}+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+7\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(-21a^{5}-13a^{4}+94a^{3}-11a^{2}-70a+25\right){x}-419a^{5}-471a^{4}+1566a^{3}+469a^{2}-861a+154$ |
| 29.1-c2 |
29.1-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-a^2-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$11538.40839$ |
1.69741 |
\( -\frac{316710223872}{707281} a^{5} + \frac{1168464334848}{707281} a^{4} - \frac{30344101888}{24389} a^{3} - \frac{599501717504}{707281} a^{2} + \frac{647902183424}{707281} a - \frac{116208054272}{707281} \) |
\( \bigl[0\) , \( 5 a^{5} - 2 a^{4} - 31 a^{3} + 17 a^{2} + 28 a - 9\) , \( 2 a^{5} - 12 a^{3} + 3 a^{2} + 12 a - 1\) , \( 12 a^{5} - 6 a^{4} - 76 a^{3} + 45 a^{2} + 70 a - 27\) , \( 2 a^{5} - 5 a^{4} - 17 a^{3} + 24 a^{2} + 19 a - 12\bigr] \) |
${y}^2+\left(2a^{5}-12a^{3}+3a^{2}+12a-1\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-31a^{3}+17a^{2}+28a-9\right){x}^{2}+\left(12a^{5}-6a^{4}-76a^{3}+45a^{2}+70a-27\right){x}+2a^{5}-5a^{4}-17a^{3}+24a^{2}+19a-12$ |
| 29.1-c3 |
29.1-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{8} \) |
$100.52490$ |
$(-a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2884.602099$ |
1.69741 |
\( -\frac{51124826476281217024}{500246412961} a^{5} + \frac{35835673211229689120}{500246412961} a^{4} + \frac{10947090981113815200}{17249876309} a^{3} - \frac{262933302104898437632}{500246412961} a^{2} - \frac{283131198263967264800}{500246412961} a + \frac{170951762512236796944}{500246412961} \) |
\( \bigl[-2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 9 a + 4\) , \( -2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 14 a + 6\) , \( 2 a^{5} - 12 a^{3} + 3 a^{2} + 12 a - 2\) , \( -a^{4} - 2 a^{3} + 2 a^{2} + 16 a - 6\) , \( 3 a^{5} - 7 a^{4} - 7 a^{3} + 28 a^{2} - 25 a + 4\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-9a+4\right){x}{y}+\left(2a^{5}-12a^{3}+3a^{2}+12a-2\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-14a+6\right){x}^{2}+\left(-a^{4}-2a^{3}+2a^{2}+16a-6\right){x}+3a^{5}-7a^{4}-7a^{3}+28a^{2}-25a+4$ |
| 29.1-c4 |
29.1-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2884.602099$ |
1.69741 |
\( \frac{47579850963904}{841} a^{5} - \frac{75268811340192}{841} a^{4} - \frac{6746732321440}{29} a^{3} + \frac{451749382000032}{841} a^{2} - \frac{253675251512576}{841} a + \frac{41182691419888}{841} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 5 a + 4\) , \( 2 a^{5} - 11 a^{3} + 3 a^{2} + 8 a - 1\) , \( 2 a^{5} - 12 a^{3} + 3 a^{2} + 12 a - 2\) , \( 30 a^{5} + 8 a^{4} - 165 a^{3} + 7 a^{2} + 106 a - 33\) , \( 86 a^{5} + 36 a^{4} - 464 a^{3} - 55 a^{2} + 262 a - 62\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-7a^{2}-5a+4\right){x}{y}+\left(2a^{5}-12a^{3}+3a^{2}+12a-2\right){y}={x}^{3}+\left(2a^{5}-11a^{3}+3a^{2}+8a-1\right){x}^{2}+\left(30a^{5}+8a^{4}-165a^{3}+7a^{2}+106a-33\right){x}+86a^{5}+36a^{4}-464a^{3}-55a^{2}+262a-62$ |
| 29.2-a1 |
29.2-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.015693237$ |
$20241.56961$ |
2.24305 |
\( \frac{196767133280}{707281} a^{5} - \frac{74008781472}{707281} a^{4} - \frac{1292726231552}{707281} a^{3} + \frac{756861293984}{707281} a^{2} + \frac{1234616501728}{707281} a - \frac{401740452496}{707281} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 18 a + 9\) , \( -3 a^{5} + a^{4} + 18 a^{3} - 10 a^{2} - 15 a + 7\) , \( -4 a^{5} + 2 a^{4} + 25 a^{3} - 16 a^{2} - 23 a + 10\) , \( -8 a^{5} + 3 a^{4} + 50 a^{3} - 29 a^{2} - 43 a + 18\) , \( -5 a^{5} + 3 a^{4} + 29 a^{3} - 19 a^{2} - 26 a + 11\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-18a+9\right){x}{y}+\left(-4a^{5}+2a^{4}+25a^{3}-16a^{2}-23a+10\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+18a^{3}-10a^{2}-15a+7\right){x}^{2}+\left(-8a^{5}+3a^{4}+50a^{3}-29a^{2}-43a+18\right){x}-5a^{5}+3a^{4}+29a^{3}-19a^{2}-26a+11$ |
| 29.2-a2 |
29.2-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.031386474$ |
$80966.27847$ |
2.24305 |
\( \frac{40448000}{841} a^{5} - \frac{86740992}{841} a^{4} - \frac{161898496}{841} a^{3} + \frac{480858112}{841} a^{2} - \frac{298524672}{841} a + \frac{54480896}{841} \) |
\( \bigl[0\) , \( -6 a^{5} + 2 a^{4} + 37 a^{3} - 19 a^{2} - 36 a + 10\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 8\) , \( 27 a^{4} - 35 a^{3} - 130 a^{2} + 214 a - 51\) , \( 98 a^{5} - 212 a^{4} - 380 a^{3} + 1173 a^{2} - 790 a + 142\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+8\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+37a^{3}-19a^{2}-36a+10\right){x}^{2}+\left(27a^{4}-35a^{3}-130a^{2}+214a-51\right){x}+98a^{5}-212a^{4}-380a^{3}+1173a^{2}-790a+142$ |
| 29.2-a3 |
29.2-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.062772949$ |
$20241.56961$ |
2.24305 |
\( -\frac{2067318144}{29} a^{5} - \frac{661386304}{29} a^{4} + \frac{11307054496}{29} a^{3} + \frac{293379616}{29} a^{2} - \frac{6717699040}{29} a + \frac{1968152368}{29} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 6 a\) , \( -4 a^{5} + 2 a^{4} + 25 a^{3} - 16 a^{2} - 24 a + 10\) , \( a + 1\) , \( 3 a^{5} - 3 a^{4} - 19 a^{3} + 21 a^{2} + 16 a - 15\) , \( 18 a^{5} - 12 a^{4} - 112 a^{3} + 89 a^{2} + 100 a - 57\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+6a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4a^{5}+2a^{4}+25a^{3}-16a^{2}-24a+10\right){x}^{2}+\left(3a^{5}-3a^{4}-19a^{3}+21a^{2}+16a-15\right){x}+18a^{5}-12a^{4}-112a^{3}+89a^{2}+100a-57$ |
| 29.2-a4 |
29.2-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.062772949$ |
$20241.56961$ |
2.24305 |
\( \frac{1470858795680}{29} a^{5} - \frac{2866574121376}{29} a^{4} - \frac{6105026493344}{29} a^{3} + \frac{16089144547520}{29} a^{2} - \frac{9383745005696}{29} a + \frac{1550049622448}{29} \) |
\( \bigl[-2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 13 a + 8\) , \( 3 a^{5} - a^{4} - 18 a^{3} + 10 a^{2} + 15 a - 5\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 10 a + 5\) , \( 3 a^{5} - 2 a^{4} - 19 a^{3} + 15 a^{2} + 19 a - 7\) , \( 4 a^{5} - 23 a^{3} + 5 a^{2} + 17 a - 5\bigr] \) |
${y}^2+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-13a+8\right){x}{y}+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-10a+5\right){y}={x}^{3}+\left(3a^{5}-a^{4}-18a^{3}+10a^{2}+15a-5\right){x}^{2}+\left(3a^{5}-2a^{4}-19a^{3}+15a^{2}+19a-7\right){x}+4a^{5}-23a^{3}+5a^{2}+17a-5$ |
| 29.2-b1 |
29.2-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.021593516$ |
$54056.33314$ |
2.06059 |
\( \frac{4891759840}{29} a^{5} + \frac{5949894240}{29} a^{4} - \frac{19788207200}{29} a^{3} - \frac{4938111360}{29} a^{2} + \frac{11563838336}{29} a - \frac{2546575952}{29} \) |
\( \bigl[-a^{5} + a^{4} + 7 a^{3} - 6 a^{2} - 8 a + 4\) , \( 3 a^{5} - a^{4} - 19 a^{3} + 10 a^{2} + 20 a - 7\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 7\) , \( 6 a^{5} - 2 a^{4} - 36 a^{3} + 20 a^{2} + 32 a - 11\) , \( 3 a^{5} - 2 a^{4} - 19 a^{3} + 15 a^{2} + 20 a - 7\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+7a^{3}-6a^{2}-8a+4\right){x}{y}+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+7\right){y}={x}^{3}+\left(3a^{5}-a^{4}-19a^{3}+10a^{2}+20a-7\right){x}^{2}+\left(6a^{5}-2a^{4}-36a^{3}+20a^{2}+32a-11\right){x}+3a^{5}-2a^{4}-19a^{3}+15a^{2}+20a-7$ |
| 29.2-b2 |
29.2-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.005398379$ |
$54056.33314$ |
2.06059 |
\( \frac{4528410113088}{707281} a^{5} - \frac{2281108973696}{707281} a^{4} - \frac{28192829925344}{707281} a^{3} + \frac{17549903182048}{707281} a^{2} + \frac{26286596217888}{707281} a - \frac{8669508625296}{707281} \) |
\( \bigl[-2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 13 a + 8\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 7 a^{2} + 13 a - 2\) , \( a^{4} - 5 a^{2} + a + 2\) , \( 9 a^{5} + 4 a^{4} - 49 a^{3} - 8 a^{2} + 30 a - 2\) , \( 11 a^{5} + 7 a^{4} - 58 a^{3} - 20 a^{2} + 30 a - 2\bigr] \) |
${y}^2+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-13a+8\right){x}{y}+\left(a^{4}-5a^{2}+a+2\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+7a^{2}+13a-2\right){x}^{2}+\left(9a^{5}+4a^{4}-49a^{3}-8a^{2}+30a-2\right){x}+11a^{5}+7a^{4}-58a^{3}-20a^{2}+30a-2$ |
| 29.2-b3 |
29.2-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.010796758$ |
$216225.3325$ |
2.06059 |
\( -\frac{29069312}{841} a^{5} + \frac{5005312}{841} a^{4} + \frac{170164224}{841} a^{3} - \frac{60727296}{841} a^{2} - \frac{122200064}{841} a + \frac{59449344}{841} \) |
\( \bigl[0\) , \( -4 a^{5} + 2 a^{4} + 25 a^{3} - 15 a^{2} - 24 a + 7\) , \( -2 a^{5} + 2 a^{4} + 13 a^{3} - 13 a^{2} - 12 a + 8\) , \( 19 a^{5} + 3 a^{4} - 110 a^{3} + 12 a^{2} + 87 a - 24\) , \( -41 a^{5} - 19 a^{4} + 222 a^{3} + 36 a^{2} - 131 a + 27\bigr] \) |
${y}^2+\left(-2a^{5}+2a^{4}+13a^{3}-13a^{2}-12a+8\right){y}={x}^{3}+\left(-4a^{5}+2a^{4}+25a^{3}-15a^{2}-24a+7\right){x}^{2}+\left(19a^{5}+3a^{4}-110a^{3}+12a^{2}+87a-24\right){x}-41a^{5}-19a^{4}+222a^{3}+36a^{2}-131a+27$ |
| 29.2-b4 |
29.2-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.021593516$ |
$54056.33314$ |
2.06059 |
\( -\frac{89927801888}{29} a^{5} - \frac{23265271776}{29} a^{4} + \frac{495788255936}{29} a^{3} - \frac{15959579104}{29} a^{2} - \frac{304802351392}{29} a + \frac{98433589296}{29} \) |
\( \bigl[-2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 9 a + 4\) , \( a^{5} - 6 a^{3} + 2 a^{2} + 5 a - 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 7 a^{2} - 3 a\) , \( -a^{4} - a^{3} + 8 a^{2} - 6 a + 1\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-9a+4\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+2\right){y}={x}^{3}+\left(a^{5}-6a^{3}+2a^{2}+5a-2\right){x}^{2}+\left(a^{5}-a^{4}-5a^{3}+7a^{2}-3a\right){x}-a^{4}-a^{3}+8a^{2}-6a+1$ |
| 29.2-c1 |
29.2-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2884.602099$ |
1.69741 |
\( \frac{137329086858432}{841} a^{5} - \frac{14691571080352}{841} a^{4} - \frac{776531184145568}{841} a^{3} + \frac{362745718807232}{841} a^{2} + \frac{689653726450208}{841} a - \frac{218133832402480}{841} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 6 a\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 8 a^{2} + 13 a - 6\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 3 a + 2\) , \( 100 a^{5} - 70 a^{4} - 621 a^{3} + 513 a^{2} + 553 a - 332\) , \( 410 a^{5} - 287 a^{4} - 2546 a^{3} + 2107 a^{2} + 2272 a - 1372\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+6a\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-3a+2\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+8a^{2}+13a-6\right){x}^{2}+\left(100a^{5}-70a^{4}-621a^{3}+513a^{2}+553a-332\right){x}+410a^{5}-287a^{4}-2546a^{3}+2107a^{2}+2272a-1372$ |
| 29.2-c2 |
29.2-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{8} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2884.602099$ |
1.69741 |
\( -\frac{409571557788112000}{500246412961} a^{5} + \frac{1366910031677275136}{500246412961} a^{4} - \frac{748134292032242112}{500246412961} a^{3} - \frac{1099915791999338272}{500246412961} a^{2} + \frac{944556414538273888}{500246412961} a - \frac{173317668143471280}{500246412961} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 18 a + 9\) , \( -5 a^{5} + 2 a^{4} + 31 a^{3} - 17 a^{2} - 30 a + 9\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 8 a^{2} - 14 a + 6\) , \( 4 a^{5} + a^{4} - 28 a^{3} + 43 a - 8\) , \( -9 a^{5} + 9 a^{4} + 50 a^{3} - 57 a^{2} - 15 a + 8\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-18a+9\right){x}{y}+\left(-2a^{5}+a^{4}+13a^{3}-8a^{2}-14a+6\right){y}={x}^{3}+\left(-5a^{5}+2a^{4}+31a^{3}-17a^{2}-30a+9\right){x}^{2}+\left(4a^{5}+a^{4}-28a^{3}+43a-8\right){x}-9a^{5}+9a^{4}+50a^{3}-57a^{2}-15a+8$ |
| 29.2-c3 |
29.2-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$11538.40839$ |
1.69741 |
\( -\frac{10818944491520}{707281} a^{5} - \frac{4799508328448}{707281} a^{4} + \frac{58185672433664}{707281} a^{3} + \frac{8469870665728}{707281} a^{2} - \frac{31983203139584}{707281} a + \frac{7316846030848}{707281} \) |
\( \bigl[0\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 9 a^{2} - 12 a + 7\) , \( -a^{5} + a^{4} + 7 a^{3} - 6 a^{2} - 7 a + 4\) , \( -8 a^{5} + 3 a^{4} + 52 a^{3} - 22 a^{2} - 54 a + 6\) , \( -15 a^{5} + 3 a^{4} + 93 a^{3} - 34 a^{2} - 93 a + 8\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+7a^{3}-6a^{2}-7a+4\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+12a^{3}-9a^{2}-12a+7\right){x}^{2}+\left(-8a^{5}+3a^{4}+52a^{3}-22a^{2}-54a+6\right){x}-15a^{5}+3a^{4}+93a^{3}-34a^{2}-93a+8$ |
| 29.2-c4 |
29.2-c |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-4a^5+2a^4+25a^3-16a^2-23a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2884.602099$ |
1.69741 |
\( -\frac{1192163968050871360}{841} a^{5} - \frac{508653899056086880}{841} a^{4} + \frac{6427305448916548704}{841} a^{3} + \frac{824459939590240608}{841} a^{2} - \frac{3592428438444074368}{841} a + \frac{835630310171383728}{841} \) |
\( \bigl[a^{5} - 6 a^{3} + 2 a^{2} + 7 a - 1\) , \( a^{2} + 2 a - 3\) , \( -a^{5} + a^{4} + 7 a^{3} - 7 a^{2} - 8 a + 6\) , \( 110 a^{5} - 80 a^{4} - 683 a^{3} + 582 a^{2} + 604 a - 379\) , \( -687 a^{5} + 462 a^{4} + 4248 a^{3} - 3450 a^{2} - 3787 a + 2236\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+2a^{2}+7a-1\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-7a^{2}-8a+6\right){y}={x}^{3}+\left(a^{2}+2a-3\right){x}^{2}+\left(110a^{5}-80a^{4}-683a^{3}+582a^{2}+604a-379\right){x}-687a^{5}+462a^{4}+4248a^{3}-3450a^{2}-3787a+2236$ |
| 29.3-a1 |
29.3-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.062772949$ |
$20241.56961$ |
2.24305 |
\( \frac{1192544800320}{29} a^{5} + \frac{1256748021376}{29} a^{4} - \frac{4574109825504}{29} a^{3} - \frac{1046658070784}{29} a^{2} + \frac{2620503823744}{29} a - \frac{580643858736}{29} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 19 a^{3} - 15 a^{2} - 18 a + 9\) , \( -2 a^{5} + 11 a^{3} - 3 a^{2} - 7 a + 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 4 a + 5\) , \( -2 a^{5} - a^{4} + 11 a^{3} + 3 a^{2} - 8 a + 1\) , \( 8 a^{5} - 6 a^{4} - 50 a^{3} + 44 a^{2} + 45 a - 30\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-15a^{2}-18a+9\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-7a^{2}-4a+5\right){y}={x}^{3}+\left(-2a^{5}+11a^{3}-3a^{2}-7a+2\right){x}^{2}+\left(-2a^{5}-a^{4}+11a^{3}+3a^{2}-8a+1\right){x}+8a^{5}-6a^{4}-50a^{3}+44a^{2}+45a-30$ |
| 29.3-a2 |
29.3-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.031386474$ |
$80966.27847$ |
2.24305 |
\( \frac{25174016}{841} a^{5} + \frac{45539328}{841} a^{4} - \frac{71008256}{841} a^{3} - \frac{87236608}{841} a^{2} + \frac{19550208}{841} a + \frac{20336640}{841} \) |
\( \bigl[0\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 7 a^{2} - 13 a + 3\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 4\) , \( -72 a^{5} + 146 a^{4} + 292 a^{3} - 815 a^{2} + 503 a - 86\) , \( -84 a^{5} + 164 a^{4} + 349 a^{3} - 920 a^{2} + 535 a - 90\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-3a+4\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+13a^{3}-7a^{2}-13a+3\right){x}^{2}+\left(-72a^{5}+146a^{4}+292a^{3}-815a^{2}+503a-86\right){x}-84a^{5}+164a^{4}+349a^{3}-920a^{2}+535a-90$ |
| 29.3-a3 |
29.3-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.015693237$ |
$20241.56961$ |
2.24305 |
\( -\frac{221274582624}{707281} a^{5} - \frac{126676391808}{707281} a^{4} + \frac{1211606023872}{707281} a^{3} + \frac{310618864480}{707281} a^{2} - \frac{803080027840}{707281} a + \frac{184207249264}{707281} \) |
\( \bigl[2 a^{5} - 12 a^{3} + 3 a^{2} + 11 a - 1\) , \( -6 a^{5} + 2 a^{4} + 37 a^{3} - 19 a^{2} - 36 a + 10\) , \( -a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 4 a + 5\) , \( 5 a^{5} + a^{4} - 37 a^{3} + 5 a^{2} + 63 a - 25\) , \( -13 a^{5} + 20 a^{4} + 61 a^{3} - 117 a^{2} + 42 a - 5\bigr] \) |
${y}^2+\left(2a^{5}-12a^{3}+3a^{2}+11a-1\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-7a^{2}-4a+5\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+37a^{3}-19a^{2}-36a+10\right){x}^{2}+\left(5a^{5}+a^{4}-37a^{3}+5a^{2}+63a-25\right){x}-13a^{5}+20a^{4}+61a^{3}-117a^{2}+42a-5$ |
| 29.3-a4 |
29.3-a |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.062772949$ |
$20241.56961$ |
2.24305 |
\( -\frac{7734027104}{29} a^{5} + \frac{5433178880}{29} a^{4} + \frac{48011782688}{29} a^{3} - \frac{39822334688}{29} a^{2} - \frac{42807379392}{29} a + \frac{25910970384}{29} \) |
\( \bigl[-2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 9 a + 4\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 4 a + 2\) , \( a^{5} - 6 a^{3} + a^{2} + 5 a + 1\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 11 a^{2} + 9 a - 5\) , \( -a^{5} - a^{4} + 7 a^{3} + 2 a^{2} - 7 a\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-9a+4\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+5a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-4a+2\right){x}^{2}+\left(a^{5}-2a^{4}-7a^{3}+11a^{2}+9a-5\right){x}-a^{5}-a^{4}+7a^{3}+2a^{2}-7a$ |
| 29.3-b1 |
29.3-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.021593516$ |
$54056.33314$ |
2.06059 |
\( \frac{84802756096}{29} a^{5} - \frac{46273500160}{29} a^{4} - \frac{534686030816}{29} a^{3} + \frac{346136614656}{29} a^{2} + \frac{520262560960}{29} a - \frac{172081078192}{29} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 25 a^{3} - 16 a^{2} - 24 a + 9\) , \( 5 a^{5} - 2 a^{4} - 31 a^{3} + 18 a^{2} + 30 a - 10\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 7\) , \( 20 a^{5} - 9 a^{4} - 123 a^{3} + 75 a^{2} + 113 a - 39\) , \( 13 a^{5} - 5 a^{4} - 81 a^{3} + 42 a^{2} + 78 a - 18\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+25a^{3}-16a^{2}-24a+9\right){x}{y}+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+7\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-31a^{3}+18a^{2}+30a-10\right){x}^{2}+\left(20a^{5}-9a^{4}-123a^{3}+75a^{2}+113a-39\right){x}+13a^{5}-5a^{4}-81a^{3}+42a^{2}+78a-18$ |
| 29.3-b2 |
29.3-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.010796758$ |
$216225.3325$ |
2.06059 |
\( -\frac{37310464}{841} a^{5} + \frac{29941760}{841} a^{4} + \frac{225488896}{841} a^{3} - \frac{219586560}{841} a^{2} - \frac{178249728}{841} a + \frac{171323392}{841} \) |
\( \bigl[0\) , \( 2 a^{5} - 11 a^{3} + 3 a^{2} + 8 a - 1\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 8 a^{2} - 14 a + 5\) , \( 28 a^{5} + 12 a^{4} - 151 a^{3} - 18 a^{2} + 87 a - 20\) , \( -165 a^{5} - 69 a^{4} + 891 a^{3} + 108 a^{2} - 500 a + 117\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-8a^{2}-14a+5\right){y}={x}^{3}+\left(2a^{5}-11a^{3}+3a^{2}+8a-1\right){x}^{2}+\left(28a^{5}+12a^{4}-151a^{3}-18a^{2}+87a-20\right){x}-165a^{5}-69a^{4}+891a^{3}+108a^{2}-500a+117$ |
| 29.3-b3 |
29.3-b |
$4$ |
$4$ |
6.6.722000.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{4} \) |
$100.52490$ |
$(-a^4+5a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.005398379$ |
$54056.33314$ |
2.06059 |
\( \frac{351210264608}{707281} a^{5} - \frac{559771119360}{707281} a^{4} - \frac{1442100814432}{707281} a^{3} + \frac{3352628507168}{707281} a^{2} - \frac{1893153182336}{707281} a + \frac{309837459664}{707281} \) |
\( \bigl[-2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 9 a + 4\) , \( -2 a^{5} + a^{4} + 12 a^{3} - 8 a^{2} - 11 a + 5\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 8 a^{2} - 14 a + 6\) , \( 50 a^{5} + 22 a^{4} - 269 a^{3} - 37 a^{2} + 148 a - 34\) , \( 233 a^{5} + 96 a^{4} - 1260 a^{3} - 144 a^{2} + 715 a - 169\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-9a+4\right){x}{y}+\left(-2a^{5}+a^{4}+13a^{3}-8a^{2}-14a+6\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+12a^{3}-8a^{2}-11a+5\right){x}^{2}+\left(50a^{5}+22a^{4}-269a^{3}-37a^{2}+148a-34\right){x}+233a^{5}+96a^{4}-1260a^{3}-144a^{2}+715a-169$ |
*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.
