| 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 |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1406.192971$ |
1.22737 |
\( -144854708632033179863920154801676 a^{5} - 71660919614753293786445158187031 a^{4} + 906870743102084208442724605571128 a^{3} + 341524848301266345855050575337161 a^{2} - 1227776258998929270457293427294949 a - 96911649208780179445472323254518 \) |
\( \bigl[-a^{5} + 7 a^{3} - 10 a + 1\) , \( -a^{4} + 6 a^{2} - a - 6\) , \( -a^{5} + 7 a^{3} - 11 a + 1\) , \( 53 a^{5} - 19 a^{4} - 351 a^{3} + 16 a^{2} + 530 a + 44\) , \( -318 a^{5} + 52 a^{4} + 2156 a^{3} + 71 a^{2} - 3332 a - 265\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-10a+1\right){x}{y}+\left(-a^{5}+7a^{3}-11a+1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-a-6\right){x}^{2}+\left(53a^{5}-19a^{4}-351a^{3}+16a^{2}+530a+44\right){x}-318a^{5}+52a^{4}+2156a^{3}+71a^{2}-3332a-265$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$22499.08754$ |
1.22737 |
\( -7060310096607968 a^{5} - 3492789392323600 a^{4} + 44201477030081336 a^{3} + 16646128858995754 a^{2} - 59842629883485619 a - 4723538002009330 \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( -a^{5} + 7 a^{3} - a^{2} - 12 a + 4\) , \( -a^{5} + 7 a^{3} - 10 a + 2\) , \( -a^{5} - 5 a^{4} + 18 a^{3} - 2 a^{2} - 23 a + 11\) , \( 9 a^{5} - 29 a^{4} + 9 a^{3} + 48 a^{2} - 46 a + 7\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+4\right){x}{y}+\left(-a^{5}+7a^{3}-10a+2\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-a^{2}-12a+4\right){x}^{2}+\left(-a^{5}-5a^{4}+18a^{3}-2a^{2}-23a+11\right){x}+9a^{5}-29a^{4}+9a^{3}+48a^{2}-46a+7$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$22499.08754$ |
1.22737 |
\( 365485502 a^{5} - 524853931 a^{4} - 1581489592 a^{3} + 2153135218 a^{2} + 240497022 a + 4303100 \) |
\( \bigl[a^{2} - 3\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 5 a^{2} + 31 a + 1\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 8 a^{5} - 62 a^{3} + 13 a^{2} + 117 a - 58\) , \( 25 a^{5} - 36 a^{4} - 152 a^{3} + 211 a^{2} + 199 a - 260\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}-5a^{2}+31a+1\right){x}^{2}+\left(8a^{5}-62a^{3}+13a^{2}+117a-58\right){x}+25a^{5}-36a^{4}-152a^{3}+211a^{2}+199a-260$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$22499.08754$ |
1.22737 |
\( -33256943880 a^{5} + 35761266300 a^{4} + 229982484868 a^{3} - 250162138391 a^{2} - 379479636676 a + 427871345244 \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 9 a - 3\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 19 a + 2\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 20 a + 4\) , \( 12 a^{5} - 18 a^{4} - 84 a^{3} + 119 a^{2} + 142 a - 192\) , \( 105 a^{5} - 116 a^{4} - 725 a^{3} + 807 a^{2} + 1195 a - 1374\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+9a-3\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+20a+4\right){y}={x}^{3}+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+19a+2\right){x}^{2}+\left(12a^{5}-18a^{4}-84a^{3}+119a^{2}+142a-192\right){x}+105a^{5}-116a^{4}-725a^{3}+807a^{2}+1195a-1374$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5624.771886$ |
1.22737 |
\( 4132241528766735571348 a^{5} + 4469525324321864971311 a^{4} - 19621826317799497716760 a^{3} - 11919544032015447856657 a^{2} + 24774907554062257500165 a + 1985106123392925227662 \) |
\( \bigl[a + 1\) , \( a^{5} + a^{4} - 8 a^{3} - 6 a^{2} + 13 a + 5\) , \( a^{5} - 6 a^{3} + 9 a + 1\) , \( -4 a^{5} + 5 a^{4} + 34 a^{3} - 28 a^{2} - 90 a - 2\) , \( -260 a^{5} - 73 a^{4} + 1732 a^{3} + 420 a^{2} - 2573 a - 200\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-6a^{3}+9a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-6a^{2}+13a+5\right){x}^{2}+\left(-4a^{5}+5a^{4}+34a^{3}-28a^{2}-90a-2\right){x}-260a^{5}-73a^{4}+1732a^{3}+420a^{2}-2573a-200$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$351.5482428$ |
1.22737 |
\( -15132807974883945943086 a^{5} + 16307180820711241349204 a^{4} + 104664146425186197661040 a^{3} - 114052056539367092574964 a^{2} - 172742751534609085925675 a + 194999297207538142410798 \) |
\( \bigl[-a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 1\) , \( 24 a^{5} + 6 a^{4} - 158 a^{3} - 25 a^{2} + 233 a - 13\) , \( 110 a^{5} - 7 a^{4} - 745 a^{3} + 13 a^{2} + 1181 a + 32\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-11a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-4a^{2}+14a\right){x}^{2}+\left(24a^{5}+6a^{4}-158a^{3}-25a^{2}+233a-13\right){x}+110a^{5}-7a^{4}-745a^{3}+13a^{2}+1181a+32$ |
| 1.1-b1 |
1.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$718.4765620$ |
0.627108 |
\( -144854708632033179863920154801676 a^{5} - 71660919614753293786445158187031 a^{4} + 906870743102084208442724605571128 a^{3} + 341524848301266345855050575337161 a^{2} - 1227776258998929270457293427294949 a - 96911649208780179445472323254518 \) |
\( \bigl[1\) , \( a^{5} + a^{4} - 8 a^{3} - 6 a^{2} + 13 a + 5\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 12 a\) , \( -48 a^{5} + 183 a^{4} + 50 a^{3} - 771 a^{2} + 622 a + 54\) , \( 988 a^{5} - 2529 a^{4} - 2647 a^{3} + 10576 a^{2} - 6040 a - 526\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+12a\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-6a^{2}+13a+5\right){x}^{2}+\left(-48a^{5}+183a^{4}+50a^{3}-771a^{2}+622a+54\right){x}+988a^{5}-2529a^{4}-2647a^{3}+10576a^{2}-6040a-526$ |
| 1.1-b2 |
1.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$11495.62499$ |
0.627108 |
\( -7060310096607968 a^{5} - 3492789392323600 a^{4} + 44201477030081336 a^{3} + 16646128858995754 a^{2} - 59842629883485619 a - 4723538002009330 \) |
\( \bigl[1\) , \( a^{5} + a^{4} - 8 a^{3} - 6 a^{2} + 13 a + 5\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 12 a\) , \( -8 a^{5} + 13 a^{4} + 35 a^{3} - 51 a^{2} - 3 a - 1\) , \( 10 a^{5} - 28 a^{4} - 26 a^{3} + 115 a^{2} - 67 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+12a\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-6a^{2}+13a+5\right){x}^{2}+\left(-8a^{5}+13a^{4}+35a^{3}-51a^{2}-3a-1\right){x}+10a^{5}-28a^{4}-26a^{3}+115a^{2}-67a-6$ |
| 1.1-b3 |
1.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2873.906248$ |
0.627108 |
\( 365485502 a^{5} - 524853931 a^{4} - 1581489592 a^{3} + 2153135218 a^{2} + 240497022 a + 4303100 \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 3\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 6\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( 9 a^{5} + 5 a^{4} - 58 a^{3} - 28 a^{2} + 80 a + 19\) , \( 19 a^{5} + 13 a^{4} - 112 a^{3} - 55 a^{2} + 144 a + 17\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+3\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4a+6\right){x}^{2}+\left(9a^{5}+5a^{4}-58a^{3}-28a^{2}+80a+19\right){x}+19a^{5}+13a^{4}-112a^{3}-55a^{2}+144a+17$ |
| 1.1-b4 |
1.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$11495.62499$ |
0.627108 |
\( -33256943880 a^{5} + 35761266300 a^{4} + 229982484868 a^{3} - 250162138391 a^{2} - 379479636676 a + 427871345244 \) |
\( \bigl[-a^{5} + 7 a^{3} - 10 a + 1\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a\) , \( a^{2} + a - 3\) , \( 32 a^{5} + 15 a^{4} - 197 a^{3} - 73 a^{2} + 265 a + 23\) , \( 96 a^{5} + 44 a^{4} - 594 a^{3} - 214 a^{2} + 797 a + 61\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-10a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a\right){x}^{2}+\left(32a^{5}+15a^{4}-197a^{3}-73a^{2}+265a+23\right){x}+96a^{5}+44a^{4}-594a^{3}-214a^{2}+797a+61$ |
| 1.1-b5 |
1.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2873.906248$ |
0.627108 |
\( 4132241528766735571348 a^{5} + 4469525324321864971311 a^{4} - 19621826317799497716760 a^{3} - 11919544032015447856657 a^{2} + 24774907554062257500165 a + 1985106123392925227662 \) |
\( \bigl[a^{3} - 3 a + 2\) , \( a^{5} - 7 a^{3} - a^{2} + 12 a + 1\) , \( a^{4} - 5 a^{2} + a + 4\) , \( 14 a^{5} - 16 a^{4} - 68 a^{3} + 69 a^{2} + 35 a - 20\) , \( 23 a^{5} - 25 a^{4} - 102 a^{3} + 102 a^{2} + 25 a - 3\bigr] \) |
${y}^2+\left(a^{3}-3a+2\right){x}{y}+\left(a^{4}-5a^{2}+a+4\right){y}={x}^{3}+\left(a^{5}-7a^{3}-a^{2}+12a+1\right){x}^{2}+\left(14a^{5}-16a^{4}-68a^{3}+69a^{2}+35a-20\right){x}+23a^{5}-25a^{4}-102a^{3}+102a^{2}+25a-3$ |
| 1.1-b6 |
1.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$102.37853$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$718.4765620$ |
0.627108 |
\( -15132807974883945943086 a^{5} + 16307180820711241349204 a^{4} + 104664146425186197661040 a^{3} - 114052056539367092574964 a^{2} - 172742751534609085925675 a + 194999297207538142410798 \) |
\( \bigl[a^{4} - 5 a^{2} + a + 5\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 6 a^{2} - 18 a - 6\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( 5 a^{5} - 3 a^{4} - 28 a^{3} + 7 a^{2} + 36 a - 6\) , \( -2 a^{5} + 17 a^{3} - 14 a^{2} - 26 a - 4\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+5\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+4\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+6a^{2}-18a-6\right){x}^{2}+\left(5a^{5}-3a^{4}-28a^{3}+7a^{2}+36a-6\right){x}-2a^{5}+17a^{3}-14a^{2}-26a-4$ |
| 4.1-a1 |
4.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2799.337221$ |
1.22167 |
\( -\frac{10576507188547681123}{64} a^{5} - \frac{2616146338735194005}{32} a^{4} + \frac{16553698917074597961}{16} a^{3} + \frac{24936296834825976631}{64} a^{2} - \frac{89645580404194791495}{64} a - \frac{3537982172908461591}{32} \) |
\( \bigl[a^{5} - 6 a^{3} + 9 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 8 a + 2\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 3\) , \( 366 a^{5} + 192 a^{4} - 2302 a^{3} - 911 a^{2} + 3138 a + 245\) , \( 4708 a^{5} + 2285 a^{4} - 29436 a^{3} - 10909 a^{2} + 39749 a + 3127\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+9a\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-8a+2\right){x}^{2}+\left(366a^{5}+192a^{4}-2302a^{3}-911a^{2}+3138a+245\right){x}+4708a^{5}+2285a^{4}-29436a^{3}-10909a^{2}+39749a+3127$ |
| 4.1-a2 |
4.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{24} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$11197.34888$ |
1.22167 |
\( -\frac{976778627465}{4096} a^{5} - \frac{483215871649}{4096} a^{4} + \frac{1528794165519}{1024} a^{3} + \frac{2302932872201}{4096} a^{2} - \frac{4139545058523}{2048} a - \frac{653446315795}{4096} \) |
\( \bigl[a + 1\) , \( -3 a^{5} - a^{4} + 20 a^{3} + 6 a^{2} - 29 a - 4\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 19 a + 1\) , \( -8 a^{5} - 5 a^{4} + 47 a^{3} + 21 a^{2} - 61 a - 8\) , \( -4 a^{5} - 2 a^{4} + 26 a^{3} + 10 a^{2} - 37 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+19a+1\right){y}={x}^{3}+\left(-3a^{5}-a^{4}+20a^{3}+6a^{2}-29a-4\right){x}^{2}+\left(-8a^{5}-5a^{4}+47a^{3}+21a^{2}-61a-8\right){x}-4a^{5}-2a^{4}+26a^{3}+10a^{2}-37a-4$ |
| 4.1-a3 |
4.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{48} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$699.8343053$ |
1.22167 |
\( \frac{150680375331}{16777216} a^{5} + \frac{35463423957}{8388608} a^{4} - \frac{235104452825}{4194304} a^{3} - \frac{339026724343}{16777216} a^{2} + \frac{1263449977415}{16777216} a + \frac{50938086903}{8388608} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a + 1\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 18 a - 4\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( 19 a^{5} + 5 a^{4} - 129 a^{3} - 25 a^{2} + 205 a + 19\) , \( -142 a^{5} - 30 a^{4} + 958 a^{3} + 168 a^{2} - 1501 a - 120\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a+1\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+4\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+5a^{2}-18a-4\right){x}^{2}+\left(19a^{5}+5a^{4}-129a^{3}-25a^{2}+205a+19\right){x}-142a^{5}-30a^{4}+958a^{3}+168a^{2}-1501a-120$ |
| 4.1-a4 |
4.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5598.674442$ |
1.22167 |
\( \frac{8454711}{8} a^{5} + \frac{9161871}{8} a^{4} - \frac{10026795}{2} a^{3} - \frac{24417263}{8} a^{2} + \frac{25303849}{4} a + \frac{4058317}{8} \) |
\( \bigl[-a^{5} + 7 a^{3} - 11 a + 1\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 9 a + 3\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a\) , \( -a^{3} - 2 a^{2} + 2 a + 7\) , \( -2 a^{5} - a^{4} + 10 a^{3} - 13 a + 4\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-11a+1\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+9a+3\right){x}^{2}+\left(-a^{3}-2a^{2}+2a+7\right){x}-2a^{5}-a^{4}+10a^{3}-13a+4$ |
| 4.1-a5 |
4.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$11197.34888$ |
1.22167 |
\( \frac{670262627}{64} a^{5} + \frac{70906485}{32} a^{4} - \frac{1129214121}{16} a^{3} - \frac{785375223}{64} a^{2} + \frac{7077786823}{64} a + \frac{276135415}{32} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 9 a + 1\) , \( a^{4} - 6 a^{2} - a + 6\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a + 1\) , \( -3 a^{5} - 2 a^{4} + 23 a^{3} + 4 a^{2} - 39 a + 6\) , \( -a^{5} - 4 a^{4} + 14 a^{3} + 11 a^{2} - 31 a + 1\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+9a+1\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a+1\right){y}={x}^{3}+\left(a^{4}-6a^{2}-a+6\right){x}^{2}+\left(-3a^{5}-2a^{4}+23a^{3}+4a^{2}-39a+6\right){x}-a^{5}-4a^{4}+14a^{3}+11a^{2}-31a+1$ |
| 4.1-a6 |
4.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$349.9171526$ |
1.22167 |
\( \frac{2598975843074521}{8} a^{5} + \frac{554714803470545}{8} a^{4} - \frac{4379915644830453}{2} a^{3} - \frac{3066240928580681}{8} a^{2} + \frac{13733388153784331}{4} a + \frac{2141808882620747}{8} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 5\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 34 a^{5} - 31 a^{4} - 253 a^{3} + 247 a^{2} + 463 a - 494\) , \( -283 a^{5} + 332 a^{4} + 1924 a^{3} - 2255 a^{2} - 3101 a + 3671\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4a+5\right){x}^{2}+\left(34a^{5}-31a^{4}-253a^{3}+247a^{2}+463a-494\right){x}-283a^{5}+332a^{4}+1924a^{3}-2255a^{2}-3101a+3671$ |
| 4.1-b1 |
4.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.017991370$ |
$17114.58316$ |
2.41882 |
\( -\frac{10576507188547681123}{64} a^{5} - \frac{2616146338735194005}{32} a^{4} + \frac{16553698917074597961}{16} a^{3} + \frac{24936296834825976631}{64} a^{2} - \frac{89645580404194791495}{64} a - \frac{3537982172908461591}{32} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{5} - 6 a^{3} - a^{2} + 7 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 69 a^{5} - 80 a^{4} - 493 a^{3} + 552 a^{2} + 835 a - 961\) , \( -828 a^{5} + 909 a^{4} + 5711 a^{3} - 6264 a^{2} - 9351 a + 10552\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+7a+4\right){x}^{2}+\left(69a^{5}-80a^{4}-493a^{3}+552a^{2}+835a-961\right){x}-828a^{5}+909a^{4}+5711a^{3}-6264a^{2}-9351a+10552$ |
| 4.1-b2 |
4.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{24} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.008995685$ |
$68458.33264$ |
2.41882 |
\( -\frac{976778627465}{4096} a^{5} - \frac{483215871649}{4096} a^{4} + \frac{1528794165519}{1024} a^{3} + \frac{2302932872201}{4096} a^{2} - \frac{4139545058523}{2048} a - \frac{653446315795}{4096} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{5} - 6 a^{3} - a^{2} + 7 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 4 a^{5} - 5 a^{4} - 28 a^{3} + 32 a^{2} + 45 a - 51\) , \( -7 a^{5} + 7 a^{4} + 47 a^{3} - 49 a^{2} - 75 a + 82\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+7a+4\right){x}^{2}+\left(4a^{5}-5a^{4}-28a^{3}+32a^{2}+45a-51\right){x}-7a^{5}+7a^{4}+47a^{3}-49a^{2}-75a+82$ |
| 4.1-b3 |
4.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{48} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.017991370$ |
$4278.645790$ |
2.41882 |
\( \frac{150680375331}{16777216} a^{5} + \frac{35463423957}{8388608} a^{4} - \frac{235104452825}{4194304} a^{3} - \frac{339026724343}{16777216} a^{2} + \frac{1263449977415}{16777216} a + \frac{50938086903}{8388608} \) |
\( \bigl[-a^{5} + 7 a^{3} + a^{2} - 11 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( a^{3} - 3 a + 2\) , \( 4 a^{5} - 6 a^{4} - 16 a^{3} + 26 a^{2} - 4 a + 1\) , \( -5 a^{5} + 17 a^{4} + 8 a^{3} - 69 a^{2} + 50 a + 5\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+a^{2}-11a-1\right){x}{y}+\left(a^{3}-3a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}^{2}+\left(4a^{5}-6a^{4}-16a^{3}+26a^{2}-4a+1\right){x}-5a^{5}+17a^{4}+8a^{3}-69a^{2}+50a+5$ |
| 4.1-b4 |
4.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.035982740$ |
$17114.58316$ |
2.41882 |
\( \frac{8454711}{8} a^{5} + \frac{9161871}{8} a^{4} - \frac{10026795}{2} a^{3} - \frac{24417263}{8} a^{2} + \frac{25303849}{4} a + \frac{4058317}{8} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 9 a + 2\) , \( a^{5} - 6 a^{3} + 8 a\) , \( -3 a^{5} - 2 a^{4} + 11 a^{3} + 3 a^{2} - 10 a + 3\) , \( -19 a^{5} - 21 a^{4} + 85 a^{3} + 54 a^{2} - 101 a - 7\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+2\right){x}{y}+\left(a^{5}-6a^{3}+8a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-9a+2\right){x}^{2}+\left(-3a^{5}-2a^{4}+11a^{3}+3a^{2}-10a+3\right){x}-19a^{5}-21a^{4}+85a^{3}+54a^{2}-101a-7$ |
| 4.1-b5 |
4.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.017991370$ |
$68458.33264$ |
2.41882 |
\( \frac{670262627}{64} a^{5} + \frac{70906485}{32} a^{4} - \frac{1129214121}{16} a^{3} - \frac{785375223}{64} a^{2} + \frac{7077786823}{64} a + \frac{276135415}{32} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 5\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 5 a^{2} + 31 a + 3\) , \( a^{4} - 4 a^{2} + 2\) , \( 3 a^{5} - 3 a^{4} - 11 a^{3} + 4 a^{2} + 7 a + 10\) , \( 4 a^{5} - 12 a^{4} - a^{3} + 31 a^{2} - 29 a + 7\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+5\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}-5a^{2}+31a+3\right){x}^{2}+\left(3a^{5}-3a^{4}-11a^{3}+4a^{2}+7a+10\right){x}+4a^{5}-12a^{4}-a^{3}+31a^{2}-29a+7$ |
| 4.1-b6 |
4.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$114.91601$ |
$(-a^5+6a^3+a^2-8a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 3 \) |
$0.035982740$ |
$4278.645790$ |
2.41882 |
\( \frac{2598975843074521}{8} a^{5} + \frac{554714803470545}{8} a^{4} - \frac{4379915644830453}{2} a^{3} - \frac{3066240928580681}{8} a^{2} + \frac{13733388153784331}{4} a + \frac{2141808882620747}{8} \) |
\( \bigl[a^{2} - 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a\) , \( a^{4} - 4 a^{2} + 1\) , \( -3 a^{5} + 25 a^{3} + 17 a^{2} - 35 a - 27\) , \( -158 a^{5} - 101 a^{4} + 940 a^{3} + 422 a^{2} - 1250 a - 147\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-4a^{2}+14a\right){x}^{2}+\left(-3a^{5}+25a^{3}+17a^{2}-35a-27\right){x}-158a^{5}-101a^{4}+940a^{3}+422a^{2}-1250a-147$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$9674.869052$ |
2.11113 |
\( -\frac{184296735}{1331} a^{5} - \frac{97588697}{1331} a^{4} + \frac{1167552003}{1331} a^{3} + \frac{458567278}{1331} a^{2} - \frac{147229616}{121} a - \frac{110571047}{1331} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 19 a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 4\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( 2 a^{5} - 15 a^{3} - a^{2} + 28 a + 6\) , \( -2 a^{5} - a^{4} + 12 a^{3} + 5 a^{2} - 15 a - 2\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+19a+3\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+9a-4\right){x}^{2}+\left(2a^{5}-15a^{3}-a^{2}+28a+6\right){x}-2a^{5}-a^{4}+12a^{3}+5a^{2}-15a-2$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{6} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$4837.434526$ |
2.11113 |
\( \frac{47528157059404}{1771561} a^{5} + \frac{10146015817896}{1771561} a^{4} - \frac{320386662079963}{1771561} a^{3} - \frac{56081952002330}{1771561} a^{2} + \frac{45662988092278}{161051} a + \frac{39177105036224}{1771561} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 8 a + 4\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a\) , \( a^{3} - 2 a + 1\) , \( -2 a^{4} - 3 a^{3} + 12 a^{2} + 8 a - 17\) , \( -a^{5} + a^{4} + 6 a^{3} - 7 a^{2} - 9 a + 11\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+8a+4\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-4a^{2}+14a\right){x}^{2}+\left(-2a^{4}-3a^{3}+12a^{2}+8a-17\right){x}-a^{5}+a^{4}+6a^{3}-7a^{2}-9a+11$ |
| 11.1-b1 |
11.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$997.9940625$ |
1.74216 |
\( \frac{6546594890726948728848}{121} a^{5} - \frac{17525444424542202235991}{121} a^{4} - \frac{16435432021021354663558}{121} a^{3} + \frac{73388910702194635258943}{121} a^{2} - \frac{4046947055903127375083}{11} a - \frac{3903679026697944289995}{121} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 8 a - 3\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 9 a - 1\) , \( -a^{5} + 7 a^{3} - 10 a + 2\) , \( 20 a^{5} - 20 a^{4} - 85 a^{3} + 50 a^{2} + 76 a + 12\) , \( -39 a^{5} + 213 a^{4} - 55 a^{3} - 603 a^{2} + 480 a + 39\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+8a-3\right){x}{y}+\left(-a^{5}+7a^{3}-10a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+9a-1\right){x}^{2}+\left(20a^{5}-20a^{4}-85a^{3}+50a^{2}+76a+12\right){x}-39a^{5}+213a^{4}-55a^{3}-603a^{2}+480a+39$ |
| 11.1-b2 |
11.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$15967.90500$ |
1.74216 |
\( \frac{24240424950436}{14641} a^{5} - \frac{64892171809942}{14641} a^{4} - \frac{60857125665148}{14641} a^{3} + \frac{271741837742300}{14641} a^{2} - \frac{14984869755639}{1331} a - \frac{14454282954729}{14641} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 8 a - 3\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 9 a - 1\) , \( -a^{5} + 7 a^{3} - 10 a + 2\) , \( -5 a^{5} - 5 a^{4} + 30 a^{3} + 15 a^{2} - 44 a + 2\) , \( -6 a^{5} + 5 a^{4} + 37 a^{3} - 9 a^{2} - 52 a - 6\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+8a-3\right){x}{y}+\left(-a^{5}+7a^{3}-10a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+9a-1\right){x}^{2}+\left(-5a^{5}-5a^{4}+30a^{3}+15a^{2}-44a+2\right){x}-6a^{5}+5a^{4}+37a^{3}-9a^{2}-52a-6$ |
| 11.1-b3 |
11.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7983.952500$ |
1.74216 |
\( \frac{8002636}{11} a^{5} + \frac{8644045}{11} a^{4} - \frac{38011268}{11} a^{3} - \frac{23029090}{11} a^{2} + 4363634 a + \frac{3785041}{11} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 19 a + 4\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 9 a + 8\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 21 a^{2} - 11 a + 32\) , \( -2 a^{5} + 3 a^{4} + 13 a^{3} - 22 a^{2} - 22 a + 36\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+19a+4\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-9a+8\right){x}^{2}+\left(-a^{5}+3a^{4}+6a^{3}-21a^{2}-11a+32\right){x}-2a^{5}+3a^{4}+13a^{3}-22a^{2}-22a+36$ |
| 11.1-b4 |
11.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{8} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3991.976250$ |
1.74216 |
\( \frac{3810109392395468}{214358881} a^{5} + \frac{3557098394492055}{214358881} a^{4} - \frac{19408197909732826}{214358881} a^{3} - \frac{9896838360006403}{214358881} a^{2} + \frac{2352619413763783}{19487171} a + \frac{2060693651777291}{214358881} \) |
\( \bigl[a + 1\) , \( -2 a^{5} + 13 a^{3} - a^{2} - 18 a + 3\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 8 a + 5\) , \( -3 a^{5} - 5 a^{4} + 25 a^{3} + 16 a^{2} - 39 a - 6\) , \( -15 a^{5} + 42 a^{4} + 17 a^{3} - 119 a^{2} + 75 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+8a+5\right){y}={x}^{3}+\left(-2a^{5}+13a^{3}-a^{2}-18a+3\right){x}^{2}+\left(-3a^{5}-5a^{4}+25a^{3}+16a^{2}-39a-6\right){x}-15a^{5}+42a^{4}+17a^{3}-119a^{2}+75a+1$ |
| 11.1-b5 |
11.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$15967.90500$ |
1.74216 |
\( -\frac{364138160}{121} a^{5} + \frac{352923496}{121} a^{4} + \frac{2507391496}{121} a^{3} - \frac{2503427015}{121} a^{2} - \frac{373192010}{11} a + \frac{4382674297}{121} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 9 a\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 1\) , \( -4 a^{5} - 5 a^{4} + 35 a^{3} + 18 a^{2} - 63 a - 5\) , \( 6 a^{5} + 6 a^{4} - 50 a^{3} - 22 a^{2} + 89 a + 7\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+11a\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-10a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+9a\right){x}^{2}+\left(-4a^{5}-5a^{4}+35a^{3}+18a^{2}-63a-5\right){x}+6a^{5}+6a^{4}-50a^{3}-22a^{2}+89a+7$ |
| 11.1-b6 |
11.1-b |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$498.9970312$ |
1.74216 |
\( -\frac{1202963448135992}{11} a^{5} + \frac{1294233223692912}{11} a^{4} + \frac{8319273703900036}{11} a^{3} - \frac{9053300969441920}{11} a^{2} - 1248006009782145 a + \frac{15483247077892477}{11} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 9 a\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 1\) , \( -59 a^{5} - 50 a^{4} + 470 a^{3} + 183 a^{2} - 823 a - 65\) , \( 531 a^{5} - 167 a^{4} - 3065 a^{3} + 222 a^{2} + 4198 a + 323\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+11a\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-10a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+9a\right){x}^{2}+\left(-59a^{5}-50a^{4}+470a^{3}+183a^{2}-823a-65\right){x}+531a^{5}-167a^{4}-3065a^{3}+222a^{2}+4198a+323$ |
| 11.1-c1 |
11.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.135896339$ |
$1842.788139$ |
2.62297 |
\( -\frac{14920576378473708}{121} a^{5} - \frac{7375406558608798}{121} a^{4} + \frac{93426338200637603}{121} a^{3} + \frac{35172990953715607}{121} a^{2} - \frac{11499142583224834}{11} a - \frac{9984165002778222}{121} \) |
\( \bigl[-a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( -a^{3} + 2 a - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 9 a + 4\) , \( 65 a^{5} - 9 a^{4} - 412 a^{3} + 86 a^{2} + 575 a - 234\) , \( -348 a^{5} + 50 a^{4} + 2275 a^{3} - 584 a^{2} - 3381 a + 1705\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+9a+4\right){y}={x}^{3}+\left(-a^{3}+2a-2\right){x}^{2}+\left(65a^{5}-9a^{4}-412a^{3}+86a^{2}+575a-234\right){x}-348a^{5}+50a^{4}+2275a^{3}-584a^{2}-3381a+1705$ |
| 11.1-c2 |
11.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.067948169$ |
$29484.61023$ |
2.62297 |
\( -\frac{94385519529}{14641} a^{5} - \frac{46056211116}{14641} a^{4} + \frac{592398546617}{14641} a^{3} + \frac{221880713424}{14641} a^{2} - \frac{72945268676}{1331} a - \frac{63298662995}{14641} \) |
\( \bigl[-a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( -a^{3} + 2 a - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 9 a + 4\) , \( 5 a^{5} + a^{4} - 37 a^{3} + a^{2} + 65 a - 24\) , \( -4 a^{5} - 4 a^{4} + 25 a^{3} + 19 a^{2} - 35 a - 11\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+9a+4\right){y}={x}^{3}+\left(-a^{3}+2a-2\right){x}^{2}+\left(5a^{5}+a^{4}-37a^{3}+a^{2}+65a-24\right){x}-4a^{5}-4a^{4}+25a^{3}+19a^{2}-35a-11$ |
| 11.1-c3 |
11.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.135896339$ |
$7371.152558$ |
2.62297 |
\( \frac{53814670}{121} a^{5} + \frac{8583009}{121} a^{4} - \frac{358364079}{121} a^{3} - \frac{51091428}{121} a^{2} + \frac{50057512}{11} a + \frac{43053739}{121} \) |
\( \bigl[-a^{5} + 7 a^{3} - 11 a + 1\) , \( a - 1\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 20 a + 4\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( -5 a^{5} - 5 a^{4} + 40 a^{3} + 18 a^{2} - 70 a - 7\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-11a+1\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+20a+4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{3}+a^{2}+2a-2\right){x}-5a^{5}-5a^{4}+40a^{3}+18a^{2}-70a-7$ |
| 11.1-c4 |
11.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.033974084$ |
$29484.61023$ |
2.62297 |
\( -\frac{5619046995486}{214358881} a^{5} + \frac{3818769223018}{214358881} a^{4} + \frac{63785965158877}{214358881} a^{3} - \frac{66431560262541}{214358881} a^{2} - \frac{15258595014700}{19487171} a + \frac{210252971634850}{214358881} \) |
\( \bigl[a + 1\) , \( a^{5} - 6 a^{3} + 8 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -3 a^{5} - 21 a^{4} + 55 a^{3} + 64 a^{2} - 128 a - 9\) , \( -14 a^{5} + 80 a^{4} - 61 a^{3} - 236 a^{2} + 277 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}+8a-1\right){x}^{2}+\left(-3a^{5}-21a^{4}+55a^{3}+64a^{2}-128a-9\right){x}-14a^{5}+80a^{4}-61a^{3}-236a^{2}+277a+22$ |
| 11.1-c5 |
11.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{16} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.067948169$ |
$1842.788139$ |
2.62297 |
\( \frac{87238696979215732687240275}{45949729863572161} a^{5} + \frac{18648780603370508150218886}{45949729863572161} a^{4} - \frac{588127547965763315875244923}{45949729863572161} a^{3} - \frac{103011645297018692140910837}{45949729863572161} a^{2} + \frac{83828286527557401115211439}{4177248169415651} a + \frac{71904962381223893462475702}{45949729863572161} \) |
\( \bigl[a^{5} - 6 a^{3} + 9 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 8 a\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( 21 a^{5} + 40 a^{4} - 185 a^{3} - 155 a^{2} + 398 a - 57\) , \( 373 a^{5} - 755 a^{4} - 1356 a^{3} + 3308 a^{2} - 813 a - 811\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+9a\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-8a\right){x}^{2}+\left(21a^{5}+40a^{4}-185a^{3}-155a^{2}+398a-57\right){x}+373a^{5}-755a^{4}-1356a^{3}+3308a^{2}-813a-811$ |
| 11.1-c6 |
11.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.067948169$ |
$7371.152558$ |
2.62297 |
\( -\frac{960900735739347}{14641} a^{5} + \frac{730755412607674}{14641} a^{4} + \frac{7485328932047243}{14641} a^{3} - \frac{6542202347616107}{14641} a^{2} - \frac{1312640100439311}{1331} a + \frac{14723389434448922}{14641} \) |
\( \bigl[a\) , \( -2 a^{5} + 13 a^{3} - a^{2} - 20 a + 3\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 8 a + 5\) , \( -65 a^{5} - 31 a^{4} + 405 a^{3} + 146 a^{2} - 545 a - 36\) , \( -529 a^{5} - 269 a^{4} + 3302 a^{3} + 1279 a^{2} - 4439 a - 352\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+8a+5\right){y}={x}^{3}+\left(-2a^{5}+13a^{3}-a^{2}-20a+3\right){x}^{2}+\left(-65a^{5}-31a^{4}+405a^{3}+146a^{2}-545a-36\right){x}-529a^{5}-269a^{4}+3302a^{3}+1279a^{2}-4439a-352$ |
| 11.1-d1 |
11.1-d |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$203.9598566$ |
1.42418 |
\( -\frac{14920576378473708}{121} a^{5} - \frac{7375406558608798}{121} a^{4} + \frac{93426338200637603}{121} a^{3} + \frac{35172990953715607}{121} a^{2} - \frac{11499142583224834}{11} a - \frac{9984165002778222}{121} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 18 a - 2\) , \( a^{5} - 6 a^{3} + 9 a\) , \( 225 a^{5} + 111 a^{4} - 1404 a^{3} - 518 a^{2} + 1905 a + 137\) , \( 2618 a^{5} + 1291 a^{4} - 16396 a^{3} - 6158 a^{2} + 22202 a + 1736\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{5}-6a^{3}+9a\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+5a^{2}-18a-2\right){x}^{2}+\left(225a^{5}+111a^{4}-1404a^{3}-518a^{2}+1905a+137\right){x}+2618a^{5}+1291a^{4}-16396a^{3}-6158a^{2}+22202a+1736$ |
| 11.1-d2 |
11.1-d |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13053.43082$ |
1.42418 |
\( -\frac{94385519529}{14641} a^{5} - \frac{46056211116}{14641} a^{4} + \frac{592398546617}{14641} a^{3} + \frac{221880713424}{14641} a^{2} - \frac{72945268676}{1331} a - \frac{63298662995}{14641} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 18 a - 2\) , \( a^{5} - 6 a^{3} + 9 a\) , \( 15 a^{5} + 11 a^{4} - 84 a^{3} - 38 a^{2} + 110 a + 7\) , \( 74 a^{5} + 45 a^{4} - 441 a^{3} - 182 a^{2} + 590 a + 47\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{5}-6a^{3}+9a\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+5a^{2}-18a-2\right){x}^{2}+\left(15a^{5}+11a^{4}-84a^{3}-38a^{2}+110a+7\right){x}+74a^{5}+45a^{4}-441a^{3}-182a^{2}+590a+47$ |
| 11.1-d3 |
11.1-d |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13053.43082$ |
1.42418 |
\( \frac{53814670}{121} a^{5} + \frac{8583009}{121} a^{4} - \frac{358364079}{121} a^{3} - \frac{51091428}{121} a^{2} + \frac{50057512}{11} a + \frac{43053739}{121} \) |
\( \bigl[a^{3} - 2 a + 2\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 6 a^{2} - 19 a - 7\) , \( a^{3} - 2 a + 2\) , \( 3 a^{5} + 3 a^{4} - 19 a^{3} - 12 a^{2} + 30 a + 8\) , \( 4 a^{5} - 5 a^{4} - 8 a^{3} + 18 a^{2} - 8 a - 7\bigr] \) |
${y}^2+\left(a^{3}-2a+2\right){x}{y}+\left(a^{3}-2a+2\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+6a^{2}-19a-7\right){x}^{2}+\left(3a^{5}+3a^{4}-19a^{3}-12a^{2}+30a+8\right){x}+4a^{5}-5a^{4}-8a^{3}+18a^{2}-8a-7$ |
| 11.1-d4 |
11.1-d |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13053.43082$ |
1.42418 |
\( -\frac{5619046995486}{214358881} a^{5} + \frac{3818769223018}{214358881} a^{4} + \frac{63785965158877}{214358881} a^{3} - \frac{66431560262541}{214358881} a^{2} - \frac{15258595014700}{19487171} a + \frac{210252971634850}{214358881} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 11 a + 4\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 18 a - 1\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a\) , \( -3 a^{5} + 20 a^{3} - a^{2} - 28 a\) , \( -3 a^{5} + a^{4} + 17 a^{3} - 4 a^{2} - 19 a - 2\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+11a+4\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a\right){y}={x}^{3}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+18a-1\right){x}^{2}+\left(-3a^{5}+20a^{3}-a^{2}-28a\right){x}-3a^{5}+a^{4}+17a^{3}-4a^{2}-19a-2$ |
| 11.1-d5 |
11.1-d |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{16} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$815.8394267$ |
1.42418 |
\( \frac{87238696979215732687240275}{45949729863572161} a^{5} + \frac{18648780603370508150218886}{45949729863572161} a^{4} - \frac{588127547965763315875244923}{45949729863572161} a^{3} - \frac{103011645297018692140910837}{45949729863572161} a^{2} + \frac{83828286527557401115211439}{4177248169415651} a + \frac{71904962381223893462475702}{45949729863572161} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 7 a + 3\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( 71 a^{5} + 68 a^{4} - 346 a^{3} - 161 a^{2} + 451 a - 20\) , \( -390 a^{5} - 366 a^{4} + 1908 a^{3} + 858 a^{2} - 2478 a + 149\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+4\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+7a+3\right){x}^{2}+\left(71a^{5}+68a^{4}-346a^{3}-161a^{2}+451a-20\right){x}-390a^{5}-366a^{4}+1908a^{3}+858a^{2}-2478a+149$ |
| 11.1-d6 |
11.1-d |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$125.02349$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3263.357706$ |
1.42418 |
\( -\frac{960900735739347}{14641} a^{5} + \frac{730755412607674}{14641} a^{4} + \frac{7485328932047243}{14641} a^{3} - \frac{6542202347616107}{14641} a^{2} - \frac{1312640100439311}{1331} a + \frac{14723389434448922}{14641} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( a^{2} - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -3 a^{5} - 2 a^{4} + 15 a^{3} + 11 a^{2} - 16 a - 15\) , \( -11 a^{5} + a^{4} + 73 a^{3} - 8 a^{2} - 113 a + 19\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-10a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{5}-2a^{4}+15a^{3}+11a^{2}-16a-15\right){x}-11a^{5}+a^{4}+73a^{3}-8a^{2}-113a+19$ |
| 11.1-e1 |
11.1-e |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.033876210$ |
$7210.632087$ |
2.55846 |
\( \frac{6546594890726948728848}{121} a^{5} - \frac{17525444424542202235991}{121} a^{4} - \frac{16435432021021354663558}{121} a^{3} + \frac{73388910702194635258943}{121} a^{2} - \frac{4046947055903127375083}{11} a - \frac{3903679026697944289995}{121} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 6 a^{2} + a + 6\) , \( a^{3} - 3 a + 2\) , \( 110 a^{5} + 72 a^{4} - 708 a^{3} - 340 a^{2} + 1015 a + 93\) , \( 802 a^{5} + 296 a^{4} - 4904 a^{3} - 1455 a^{2} + 6306 a + 506\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a+2\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+6\right){x}^{2}+\left(110a^{5}+72a^{4}-708a^{3}-340a^{2}+1015a+93\right){x}+802a^{5}+296a^{4}-4904a^{3}-1455a^{2}+6306a+506$ |
| 11.1-e2 |
11.1-e |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.016938105$ |
$115370.1134$ |
2.55846 |
\( \frac{24240424950436}{14641} a^{5} - \frac{64892171809942}{14641} a^{4} - \frac{60857125665148}{14641} a^{3} + \frac{271741837742300}{14641} a^{2} - \frac{14984869755639}{1331} a - \frac{14454282954729}{14641} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 6 a^{2} + a + 6\) , \( a^{3} - 3 a + 2\) , \( 10 a^{5} + 7 a^{4} - 63 a^{3} - 35 a^{2} + 85 a + 18\) , \( -9 a^{5} - 6 a^{4} + 59 a^{3} + 26 a^{2} - 88 a\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a+2\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+6\right){x}^{2}+\left(10a^{5}+7a^{4}-63a^{3}-35a^{2}+85a+18\right){x}-9a^{5}-6a^{4}+59a^{3}+26a^{2}-88a$ |
| 11.1-e3 |
11.1-e |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.067752420$ |
$28842.52835$ |
2.55846 |
\( \frac{8002636}{11} a^{5} + \frac{8644045}{11} a^{4} - \frac{38011268}{11} a^{3} - \frac{23029090}{11} a^{2} + 4363634 a + \frac{3785041}{11} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 3\) , \( -a^{4} + 4 a^{2} + a - 1\) , \( -a^{5} + 7 a^{3} - 11 a + 2\) , \( 2 a^{5} - 2 a^{4} - 15 a^{3} + 11 a^{2} + 26 a - 10\) , \( -3 a^{2} + 10\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+3\right){x}{y}+\left(-a^{5}+7a^{3}-11a+2\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-1\right){x}^{2}+\left(2a^{5}-2a^{4}-15a^{3}+11a^{2}+26a-10\right){x}-3a^{2}+10$ |
| 11.1-e4 |
11.1-e |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{8} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.008469052$ |
$28842.52835$ |
2.55846 |
\( \frac{3810109392395468}{214358881} a^{5} + \frac{3557098394492055}{214358881} a^{4} - \frac{19408197909732826}{214358881} a^{3} - \frac{9896838360006403}{214358881} a^{2} + \frac{2352619413763783}{19487171} a + \frac{2060693651777291}{214358881} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{3} - 2 a\) , \( a^{3} - 2 a + 1\) , \( -10 a^{5} - 13 a^{4} + 79 a^{3} + 43 a^{2} - 119 a - 10\) , \( -55 a^{5} + 127 a^{4} + 102 a^{3} - 339 a^{2} + 145 a + 13\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(-10a^{5}-13a^{4}+79a^{3}+43a^{2}-119a-10\right){x}-55a^{5}+127a^{4}+102a^{3}-339a^{2}+145a+13$ |
| 11.1-e5 |
11.1-e |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.033876210$ |
$115370.1134$ |
2.55846 |
\( -\frac{364138160}{121} a^{5} + \frac{352923496}{121} a^{4} + \frac{2507391496}{121} a^{3} - \frac{2503427015}{121} a^{2} - \frac{373192010}{11} a + \frac{4382674297}{121} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 8 a + 4\) , \( a^{5} + a^{4} - 8 a^{3} - 5 a^{2} + 14 a + 3\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( -a^{5} - 2 a^{4} + 9 a^{3} + 7 a^{2} - 17 a - 3\) , \( -5 a^{5} - 2 a^{4} + 35 a^{3} + 9 a^{2} - 56 a - 6\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+8a+4\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+4\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-5a^{2}+14a+3\right){x}^{2}+\left(-a^{5}-2a^{4}+9a^{3}+7a^{2}-17a-3\right){x}-5a^{5}-2a^{4}+35a^{3}+9a^{2}-56a-6$ |
| 11.1-e6 |
11.1-e |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$125.02349$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.067752420$ |
$7210.632087$ |
2.55846 |
\( -\frac{1202963448135992}{11} a^{5} + \frac{1294233223692912}{11} a^{4} + \frac{8319273703900036}{11} a^{3} - \frac{9053300969441920}{11} a^{2} - 1248006009782145 a + \frac{15483247077892477}{11} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 5\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 4\) , \( 1\) , \( 18 a^{5} - 59 a^{4} - 7 a^{3} + 168 a^{2} - 115 a - 17\) , \( 232 a^{5} - 698 a^{4} - 224 a^{3} + 2072 a^{2} - 1346 a - 115\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+5\right){x}{y}+{y}={x}^{3}+\left(a^{5}-6a^{3}+a^{2}+7a-4\right){x}^{2}+\left(18a^{5}-59a^{4}-7a^{3}+168a^{2}-115a-17\right){x}+232a^{5}-698a^{4}-224a^{3}+2072a^{2}-1346a-115$ |
*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.
