| 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 |
| 19.1-a1 |
19.1-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1.391637733$ |
$297.0176190$ |
3.14685 |
\( \frac{164927433229853589}{47045881} a^{5} - \frac{462048753724117587}{47045881} a^{4} - \frac{586486265849135487}{47045881} a^{3} + \frac{1532873006546783733}{47045881} a^{2} + \frac{799015604456749284}{47045881} a - \frac{830982177318641229}{47045881} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -a^{4} + 4 a^{3} - 9 a + 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 7 a - 4\) , \( 6 a^{5} - 27 a^{4} + 22 a^{3} + 34 a^{2} - 40 a + 8\) , \( 23 a^{5} - 100 a^{4} + 68 a^{3} + 132 a^{2} - 108 a + 14\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+7a-4\right){y}={x}^{3}+\left(-a^{4}+4a^{3}-9a+2\right){x}^{2}+\left(6a^{5}-27a^{4}+22a^{3}+34a^{2}-40a+8\right){x}+23a^{5}-100a^{4}+68a^{3}+132a^{2}-108a+14$ |
| 19.1-a2 |
19.1-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.463879244$ |
$24058.42713$ |
3.14685 |
\( -\frac{119309721039}{361} a^{5} + \frac{491154651756}{361} a^{4} - \frac{190507518108}{361} a^{3} - \frac{980379356040}{361} a^{2} + \frac{736788395997}{361} a - \frac{106850556567}{361} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( a^{4} - 3 a^{3} + 5 a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 3\) , \( -2 a^{5} + 8 a^{4} - a^{3} - 17 a^{2} + 5 a\) , \( 3 a^{5} - 11 a^{4} + 2 a^{3} + 23 a^{2} - 15 a + 1\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-4\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-3\right){y}={x}^{3}+\left(a^{4}-3a^{3}+5a-4\right){x}^{2}+\left(-2a^{5}+8a^{4}-a^{3}-17a^{2}+5a\right){x}+3a^{5}-11a^{4}+2a^{3}+23a^{2}-15a+1$ |
| 19.1-a3 |
19.1-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.927758489$ |
$24058.42713$ |
3.14685 |
\( \frac{15934214875439431467}{19} a^{5} - \frac{65595149908150910652}{19} a^{4} + \frac{25442385660496971315}{19} a^{3} + \frac{130932604596100200840}{19} a^{2} - \frac{98399667624912226827}{19} a + \frac{14270008618918755090}{19} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( a^{4} - 3 a^{3} + 5 a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 3\) , \( -22 a^{5} + 88 a^{4} - 31 a^{3} - 177 a^{2} + 135 a - 25\) , \( 136 a^{5} - 557 a^{4} + 212 a^{3} + 1114 a^{2} - 835 a + 119\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-4\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-3\right){y}={x}^{3}+\left(a^{4}-3a^{3}+5a-4\right){x}^{2}+\left(-22a^{5}+88a^{4}-31a^{3}-177a^{2}+135a-25\right){x}+136a^{5}-557a^{4}+212a^{3}+1114a^{2}-835a+119$ |
| 19.1-a4 |
19.1-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$2.783275467$ |
$297.0176190$ |
3.14685 |
\( -\frac{315489639444944728535955}{6859} a^{5} + \frac{883852718862278089035207}{6859} a^{4} + \frac{1121889886979135975018910}{6859} a^{3} - \frac{2932231456631342131141563}{6859} a^{2} - \frac{1528437917733169511460384}{6859} a + \frac{1589584060278264112361901}{6859} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 2\) , \( a^{3} - 2 a^{2} - a + 3\) , \( -2242 a^{5} + 9242 a^{4} - 3600 a^{3} - 18449 a^{2} + 13877 a - 2020\) , \( 116961 a^{5} - 481457 a^{4} + 186714 a^{3} + 961018 a^{2} - 722217 a + 104730\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-2a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+4a-2\right){x}^{2}+\left(-2242a^{5}+9242a^{4}-3600a^{3}-18449a^{2}+13877a-2020\right){x}+116961a^{5}-481457a^{4}+186714a^{3}+961018a^{2}-722217a+104730$ |
| 19.1-b1 |
19.1-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.235711397$ |
$14160.16121$ |
2.82341 |
\( \frac{164927433229853589}{47045881} a^{5} - \frac{462048753724117587}{47045881} a^{4} - \frac{586486265849135487}{47045881} a^{3} + \frac{1532873006546783733}{47045881} a^{2} + \frac{799015604456749284}{47045881} a - \frac{830982177318641229}{47045881} \) |
\( \bigl[a^{4} - 3 a^{3} + 5 a - 2\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 12 a^{2} + 4 a - 8\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a\) , \( -38 a^{5} + 90 a^{4} + 175 a^{3} - 289 a^{2} - 287 a + 81\) , \( 203 a^{5} - 487 a^{4} - 910 a^{3} + 1515 a^{2} + 1510 a - 361\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}+5a-2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+12a^{2}+4a-8\right){x}^{2}+\left(-38a^{5}+90a^{4}+175a^{3}-289a^{2}-287a+81\right){x}+203a^{5}-487a^{4}-910a^{3}+1515a^{2}+1510a-361$ |
| 19.1-b2 |
19.1-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.707134191$ |
$1573.351246$ |
2.82341 |
\( -\frac{119309721039}{361} a^{5} + \frac{491154651756}{361} a^{4} - \frac{190507518108}{361} a^{3} - \frac{980379356040}{361} a^{2} + \frac{736788395997}{361} a - \frac{106850556567}{361} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 2\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( 0\) , \( -3 a^{5} + 11 a^{4} - 2 a^{3} - 18 a^{2} + 5 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-2\right){x}{y}={x}^{3}+\left(-a^{3}+3a^{2}+a-4\right){x}^{2}+\left(-3a^{5}+11a^{4}-2a^{3}-18a^{2}+5a+3\right){x}$ |
| 19.1-b3 |
19.1-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.414268383$ |
$1573.351246$ |
2.82341 |
\( \frac{15934214875439431467}{19} a^{5} - \frac{65595149908150910652}{19} a^{4} + \frac{25442385660496971315}{19} a^{3} + \frac{130932604596100200840}{19} a^{2} - \frac{98399667624912226827}{19} a + \frac{14270008618918755090}{19} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 10 a - 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a - 1\) , \( 0\) , \( -32 a^{5} + 80 a^{4} + 132 a^{3} - 240 a^{2} - 212 a + 48\) , \( 31 a^{5} - 58 a^{4} - 195 a^{3} + 218 a^{2} + 361 a - 75\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+10a-4\right){x}{y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-7a-1\right){x}^{2}+\left(-32a^{5}+80a^{4}+132a^{3}-240a^{2}-212a+48\right){x}+31a^{5}-58a^{4}-195a^{3}+218a^{2}+361a-75$ |
| 19.1-b4 |
19.1-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$135.01318$ |
$(a^5-3a^4-2a^3+8a^2+a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.471422794$ |
$14160.16121$ |
2.82341 |
\( -\frac{315489639444944728535955}{6859} a^{5} + \frac{883852718862278089035207}{6859} a^{4} + \frac{1121889886979135975018910}{6859} a^{3} - \frac{2932231456631342131141563}{6859} a^{2} - \frac{1528437917733169511460384}{6859} a + \frac{1589584060278264112361901}{6859} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a - 1\) , \( 80 a^{5} - 81 a^{4} - 398 a^{3} + 24 a^{2} + 255 a - 68\) , \( 222 a^{5} - 155 a^{4} - 1189 a^{3} - 212 a^{2} + 667 a - 78\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+3a-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-3\right){x}^{2}+\left(80a^{5}-81a^{4}-398a^{3}+24a^{2}+255a-68\right){x}+222a^{5}-155a^{4}-1189a^{3}-212a^{2}+667a-78$ |
| 19.2-a1 |
19.2-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$135.01318$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.927758489$ |
$24058.42713$ |
3.14685 |
\( \frac{30438798074416398357}{19} a^{5} - \frac{73523888941416578820}{19} a^{4} - \frac{134293589945377162173}{19} a^{3} + \frac{225888842823227670348}{19} a^{2} + \frac{223356050294960948895}{19} a - \frac{52073635140874193409}{19} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 9 a - 5\) , \( 61 a^{5} - 52 a^{4} - 294 a^{3} - 54 a^{2} + 119 a - 22\) , \( -385 a^{5} + 338 a^{4} + 1905 a^{3} + 207 a^{2} - 929 a + 163\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+9a-5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(61a^{5}-52a^{4}-294a^{3}-54a^{2}+119a-22\right){x}-385a^{5}+338a^{4}+1905a^{3}+207a^{2}-929a+163$ |
| 19.2-a2 |
19.2-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$135.01318$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$2.783275467$ |
$297.0176190$ |
3.14685 |
\( \frac{23356303984655729540145}{6859} a^{5} - \frac{7452712481411092047777}{6859} a^{4} - \frac{90048979498873307140854}{6859} a^{3} - \frac{7850364710050201601979}{6859} a^{2} + \frac{49022773693222173695892}{6859} a - \frac{8712073558822488019641}{6859} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 10 a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a\) , \( -47 a^{5} + 97 a^{4} + 278 a^{3} - 375 a^{2} - 479 a + 89\) , \( 342 a^{5} - 795 a^{4} - 1606 a^{3} + 2521 a^{2} + 2619 a - 626\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+10a-4\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-4\right){x}^{2}+\left(-47a^{5}+97a^{4}+278a^{3}-375a^{2}-479a+89\right){x}+342a^{5}-795a^{4}-1606a^{3}+2521a^{2}+2619a-626$ |
| 19.2-a3 |
19.2-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$135.01318$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1.391637733$ |
$297.0176190$ |
3.14685 |
\( -\frac{12210045787883583}{47045881} a^{5} + \frac{3896591398207569}{47045881} a^{4} + \frac{47074450079680857}{47045881} a^{3} + \frac{4102787318035545}{47045881} a^{2} - \frac{25626747801780036}{47045881} a + \frac{4554281634804891}{47045881} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 8 a - 2\) , \( -a^{5} + 4 a^{4} - 11 a^{2} + 2 a + 3\) , \( a^{3} - a^{2} - 3 a\) , \( 5 a^{5} - 8 a^{4} - 20 a^{3} + 10 a^{2} + 12 a\) , \( 11 a^{5} - 10 a^{4} - 56 a^{3} - 2 a^{2} + 33 a - 6\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+6a^{2}+8a-2\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-11a^{2}+2a+3\right){x}^{2}+\left(5a^{5}-8a^{4}-20a^{3}+10a^{2}+12a\right){x}+11a^{5}-10a^{4}-56a^{3}-2a^{2}+33a-6$ |
| 19.2-a4 |
19.2-a |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$135.01318$ |
$(-a^2+a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.463879244$ |
$24058.42713$ |
3.14685 |
\( -\frac{227915510049}{361} a^{5} + \frac{550521041508}{361} a^{4} + \frac{1005549589422}{361} a^{3} - \frac{1691380479852}{361} a^{2} - \frac{1672422076449}{361} a + \frac{389911279446}{361} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 9 a - 5\) , \( -14 a^{5} + 13 a^{4} + 71 a^{3} + a^{2} - 41 a + 8\) , \( -70 a^{5} + 64 a^{4} + 349 a^{3} + 20 a^{2} - 187 a + 31\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+9a-5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-14a^{5}+13a^{4}+71a^{3}+a^{2}-41a+8\right){x}-70a^{5}+64a^{4}+349a^{3}+20a^{2}-187a+31$ |
| 19.2-b1 |
19.2-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$135.01318$ |
$(-a^2+a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 1 \) |
$1$ |
$1573.351246$ |
2.82341 |
\( \frac{30438798074416398357}{19} a^{5} - \frac{73523888941416578820}{19} a^{4} - \frac{134293589945377162173}{19} a^{3} + \frac{225888842823227670348}{19} a^{2} + \frac{223356050294960948895}{19} a - \frac{52073635140874193409}{19} \) |
\( \bigl[a^{4} - 3 a^{3} - a^{2} + 6 a - 1\) , \( a^{4} - 4 a^{3} + 9 a - 1\) , \( 0\) , \( -20 a^{5} + 76 a^{4} - 8 a^{3} - 164 a^{2} + 68 a - 8\) , \( 3 a^{5} - 44 a^{4} + 119 a^{3} + 36 a^{2} - 277 a + 52\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-a^{2}+6a-1\right){x}{y}={x}^{3}+\left(a^{4}-4a^{3}+9a-1\right){x}^{2}+\left(-20a^{5}+76a^{4}-8a^{3}-164a^{2}+68a-8\right){x}+3a^{5}-44a^{4}+119a^{3}+36a^{2}-277a+52$ |
| 19.2-b2 |
19.2-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$135.01318$ |
$(-a^2+a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 3 \) |
$1$ |
$14160.16121$ |
2.82341 |
\( \frac{23356303984655729540145}{6859} a^{5} - \frac{7452712481411092047777}{6859} a^{4} - \frac{90048979498873307140854}{6859} a^{3} - \frac{7850364710050201601979}{6859} a^{2} + \frac{49022773693222173695892}{6859} a - \frac{8712073558822488019641}{6859} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( -a^{4} + 4 a^{3} - 2 a^{2} - 7 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( 2 a^{5} - 104 a^{4} + 135 a^{3} + 202 a^{2} - 111 a - 20\) , \( 368 a^{5} - 56 a^{4} - 1473 a^{3} - 288 a^{2} + 785 a - 89\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-4\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(-a^{4}+4a^{3}-2a^{2}-7a+5\right){x}^{2}+\left(2a^{5}-104a^{4}+135a^{3}+202a^{2}-111a-20\right){x}+368a^{5}-56a^{4}-1473a^{3}-288a^{2}+785a-89$ |
| 19.2-b3 |
19.2-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$135.01318$ |
$(-a^2+a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2 \cdot 3 \) |
$1$ |
$14160.16121$ |
2.82341 |
\( -\frac{12210045787883583}{47045881} a^{5} + \frac{3896591398207569}{47045881} a^{4} + \frac{47074450079680857}{47045881} a^{3} + \frac{4102787318035545}{47045881} a^{2} - \frac{25626747801780036}{47045881} a + \frac{4554281634804891}{47045881} \) |
\( \bigl[a\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 11 a^{2} + 7 a - 4\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 10 a - 4\) , \( -105 a^{5} + 429 a^{4} - 160 a^{3} - 856 a^{2} + 635 a - 90\) , \( 1119 a^{5} - 4610 a^{4} + 1797 a^{3} + 9200 a^{2} - 6931 a + 1005\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+10a-4\right){y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+11a^{2}+7a-4\right){x}^{2}+\left(-105a^{5}+429a^{4}-160a^{3}-856a^{2}+635a-90\right){x}+1119a^{5}-4610a^{4}+1797a^{3}+9200a^{2}-6931a+1005$ |
| 19.2-b4 |
19.2-b |
$4$ |
$6$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$135.01318$ |
$(-a^2+a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2 \) |
$1$ |
$1573.351246$ |
2.82341 |
\( -\frac{227915510049}{361} a^{5} + \frac{550521041508}{361} a^{4} + \frac{1005549589422}{361} a^{3} - \frac{1691380479852}{361} a^{2} - \frac{1672422076449}{361} a + \frac{389911279446}{361} \) |
\( \bigl[a^{4} - 3 a^{3} - a^{2} + 6 a - 1\) , \( a^{4} - 4 a^{3} + 9 a - 1\) , \( 0\) , \( 5 a^{5} - 19 a^{4} + 2 a^{3} + 41 a^{2} - 17 a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-a^{2}+6a-1\right){x}{y}={x}^{3}+\left(a^{4}-4a^{3}+9a-1\right){x}^{2}+\left(5a^{5}-19a^{4}+2a^{3}+41a^{2}-17a+2\right){x}$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$2084.124108$ |
1.76299 |
\( 2650612900 a^{5} - 11822464871 a^{4} + 8994313273 a^{3} + 14585431444 a^{2} - 13645170031 a + 2080864404 \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{5} - 4 a^{4} + a^{3} + 7 a^{2} - 3 a + 3\) , \( a^{4} - 3 a^{3} + 6 a - 3\) , \( 3 a^{5} - 14 a^{4} + 11 a^{3} + 15 a^{2} - 8 a - 2\) , \( 12 a^{5} - 56 a^{4} + 50 a^{3} + 62 a^{2} - 76 a + 19\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+1\right){x}{y}+\left(a^{4}-3a^{3}+6a-3\right){y}={x}^{3}+\left(a^{5}-4a^{4}+a^{3}+7a^{2}-3a+3\right){x}^{2}+\left(3a^{5}-14a^{4}+11a^{3}+15a^{2}-8a-2\right){x}+12a^{5}-56a^{4}+50a^{3}+62a^{2}-76a+19$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.065830368$ |
$96464.23212$ |
3.58118 |
\( -2106 a^{5} + 14985 a^{4} - 32940 a^{3} + 10125 a^{2} + 43254 a - 35397 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 15 a^{2} - 6 a + 9\) , \( -a^{5} + 4 a^{4} + a^{3} - 12 a^{2} - 2 a + 4\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-3\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+3\right){x}^{2}+\left(-2a^{5}+5a^{4}+7a^{3}-15a^{2}-6a+9\right){x}-a^{5}+4a^{4}+a^{3}-12a^{2}-2a+4$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.197491106$ |
$1190.916445$ |
3.58118 |
\( 31337523 a^{5} - 128952081 a^{4} + 49925556 a^{3} + 257372748 a^{2} - 193378914 a + 28043883 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a - 1\) , \( a^{2} - 1\) , \( 6 a^{5} - 13 a^{4} - 32 a^{3} + 45 a^{2} + 58 a - 13\) , \( 9 a^{5} - 20 a^{4} - 46 a^{3} + 65 a^{2} + 79 a - 18\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a-1\right){x}^{2}+\left(6a^{5}-13a^{4}-32a^{3}+45a^{2}+58a-13\right){x}+9a^{5}-20a^{4}-46a^{3}+65a^{2}+79a-18$ |
| 27.1-c1 |
27.1-c |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$26.63820562$ |
1.82522 |
\( -6771084180533076891 a^{5} + 29803747663716890662 a^{4} - 21460311949981464275 a^{3} - 37631613737255724066 a^{2} + 32432015039181408419 a - 4830894579990068812 \) |
\( \bigl[a^{4} - 3 a^{3} - a^{2} + 7 a - 1\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 10 a^{2} - 13 a + 6\) , \( a^{3} - a^{2} - 2 a\) , \( 38 a^{4} - 148 a^{3} + 30 a^{2} + 319 a - 173\) , \( -117 a^{5} + 696 a^{4} - 997 a^{3} - 823 a^{2} + 2446 a - 1024\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-a^{2}+7a-1\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-10a^{2}-13a+6\right){x}^{2}+\left(38a^{4}-148a^{3}+30a^{2}+319a-173\right){x}-117a^{5}+696a^{4}-997a^{3}-823a^{2}+2446a-1024$ |
| 27.1-c2 |
27.1-c |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$19419.25189$ |
1.82522 |
\( -371835 a^{5} + 1522665 a^{4} - 988206 a^{3} - 1890837 a^{2} + 1592604 a - 238485 \) |
\( \bigl[a^{4} - 3 a^{3} - a^{2} + 7 a - 1\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 10 a^{2} - 13 a + 6\) , \( a^{3} - a^{2} - 2 a\) , \( -2 a^{4} + 2 a^{3} + 5 a^{2} - a + 2\) , \( -1\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-a^{2}+7a-1\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-10a^{2}-13a+6\right){x}^{2}+\left(-2a^{4}+2a^{3}+5a^{2}-a+2\right){x}-1$ |
| 27.1-c3 |
27.1-c |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$19419.25189$ |
1.82522 |
\( -58952752457488515 a^{5} + 18809935951457923 a^{4} + 227290860824076541 a^{3} + 19817440623237963 a^{2} - 123739055493356554 a + 21990202152668141 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{4} - 4 a^{3} + a^{2} + 9 a - 4\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -157 a^{5} + 464 a^{4} + 463 a^{3} - 1438 a^{2} - 556 a + 678\) , \( -608 a^{5} + 1548 a^{4} + 2771 a^{3} - 5779 a^{2} - 4248 a + 3766\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-4a^{3}+a^{2}+9a-4\right){x}^{2}+\left(-157a^{5}+464a^{4}+463a^{3}-1438a^{2}-556a+678\right){x}-608a^{5}+1548a^{4}+2771a^{3}-5779a^{2}-4248a+3766$ |
| 27.1-d1 |
27.1-d |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.197491106$ |
$1190.916445$ |
3.58118 |
\( 59860377 a^{5} - 144641619 a^{4} - 263914785 a^{3} + 444199410 a^{2} + 438961572 a - 102352338 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 3\) , \( a^{5} - 7 a^{4} + 10 a^{3} + 14 a^{2} - 23 a + 2\) , \( 2 a^{5} - 10 a^{4} + 7 a^{3} + 21 a^{2} - 18 a + 1\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-5a^{2}-8a+1\right){x}^{2}+\left(a^{5}-7a^{4}+10a^{3}+14a^{2}-23a+2\right){x}+2a^{5}-10a^{4}+7a^{3}+21a^{2}-18a+1$ |
| 27.1-d2 |
27.1-d |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.065830368$ |
$96464.23212$ |
3.58118 |
\( -6399 a^{5} + 10530 a^{4} + 20709 a^{3} - 11178 a^{2} - 1782 a + 1674 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 10 a - 5\) , \( -17 a^{5} + 66 a^{4} - 15 a^{3} - 135 a^{2} + 81 a - 7\) , \( 57 a^{5} - 234 a^{4} + 87 a^{3} + 471 a^{2} - 341 a + 47\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+10a-5\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-5a^{2}-8a+1\right){x}^{2}+\left(-17a^{5}+66a^{4}-15a^{3}-135a^{2}+81a-7\right){x}+57a^{5}-234a^{4}+87a^{3}+471a^{2}-341a+47$ |
| 27.1-e1 |
27.1-e |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$19419.25189$ |
1.82522 |
\( 796320068330093137 a^{5} - 2230911883569271789 a^{4} - 2831736699761517383 a^{3} + 7401176184869457587 a^{2} + 3857896101623028994 a - 4012230232721862853 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} - a^{3} + 12 a^{2} - a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 3\) , \( -26 a^{5} + 83 a^{4} + 128 a^{3} - 275 a^{2} - 264 a + 63\) , \( 204 a^{5} - 422 a^{4} - 876 a^{3} + 1247 a^{2} + 1306 a - 299\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-3\right){y}={x}^{3}+\left(a^{5}-4a^{4}-a^{3}+12a^{2}-a-4\right){x}^{2}+\left(-26a^{5}+83a^{4}+128a^{3}-275a^{2}-264a+63\right){x}+204a^{5}-422a^{4}-876a^{3}+1247a^{2}+1306a-299$ |
| 27.1-e2 |
27.1-e |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$19419.25189$ |
1.82522 |
\( 151731 a^{5} - 862353 a^{4} - 214320 a^{3} + 3635577 a^{2} + 1252656 a - 1827213 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a\) , \( 1\) , \( 2 a^{5} - 6 a^{4} - 2 a^{3} + 13 a^{2} - 5 a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-8a\right){x}^{2}+\left(2a^{5}-6a^{4}-2a^{3}+13a^{2}-5a\right){x}+2a^{5}-5a^{4}-5a^{3}+11a^{2}+2a$ |
| 27.1-e3 |
27.1-e |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$26.63820562$ |
1.82522 |
\( -4619763599211458927 a^{5} + 4368795675516716792 a^{4} + 22834216279555443787 a^{3} + 711261738874157588 a^{2} - 12398128138840295807 a + 2248798976045317301 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a\) , \( 1\) , \( 17 a^{5} - 6 a^{4} - 77 a^{3} - 72 a^{2} - 20 a + 10\) , \( 217 a^{5} - 188 a^{4} - 1059 a^{3} - 159 a^{2} + 471 a - 76\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-8a\right){x}^{2}+\left(17a^{5}-6a^{4}-77a^{3}-72a^{2}-20a+10\right){x}+217a^{5}-188a^{4}-1059a^{3}-159a^{2}+471a-76$ |
| 27.1-f1 |
27.1-f |
$1$ |
$1$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$2084.124108$ |
1.76299 |
\( 1820884570 a^{5} - 1592027539 a^{4} - 9268094856 a^{3} - 623375868 a^{2} + 5249738257 a - 943012354 \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 2 a - 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 4\) , \( -8 a^{5} + 26 a^{4} + 29 a^{3} - 87 a^{2} - 67 a + 20\) , \( 26 a^{5} - 47 a^{4} - 122 a^{3} + 117 a^{2} + 147 a - 34\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-4\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+2a-4\right){x}^{2}+\left(-8a^{5}+26a^{4}+29a^{3}-87a^{2}-67a+20\right){x}+26a^{5}-47a^{4}-122a^{3}+117a^{2}+147a-34$ |
| 27.1-g1 |
27.1-g |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$20586.05256$ |
1.93489 |
\( -20571839670924 a^{5} + 84686501192643 a^{4} - 32847346580697 a^{3} - 169040305433673 a^{2} + 127038715216011 a - 18423269152983 \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 22 a^{5} - 65 a^{4} - 65 a^{3} + 197 a^{2} + 90 a - 101\) , \( 72 a^{5} - 194 a^{4} - 292 a^{3} + 692 a^{2} + 403 a - 396\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(22a^{5}-65a^{4}-65a^{3}+197a^{2}+90a-101\right){x}+72a^{5}-194a^{4}-292a^{3}+692a^{2}+403a-396$ |
| 27.1-g2 |
27.1-g |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2287.339174$ |
1.93489 |
\( 8199093861 a^{5} - 22969972953 a^{4} - 29156241303 a^{3} + 76204224981 a^{2} + 39721845717 a - 41310902691 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 3 a - 5\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 4 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 10 a^{5} - 27 a^{4} - 40 a^{3} + 95 a^{2} + 55 a - 51\) , \( 58 a^{5} - 164 a^{4} - 201 a^{3} + 538 a^{2} + 273 a - 291\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+3a-5\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-9a^{2}-4a+2\right){x}^{2}+\left(10a^{5}-27a^{4}-40a^{3}+95a^{2}+55a-51\right){x}+58a^{5}-164a^{4}-201a^{3}+538a^{2}+273a-291$ |
| 27.1-h1 |
27.1-h |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17180.22660$ |
1.61477 |
\( -607008006 a^{5} + 193715388 a^{4} + 2340294876 a^{3} + 203925438 a^{2} - 1274124573 a + 226434609 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 10 a - 2\) , \( a^{2} - 1\) , \( 4 a^{5} - 12 a^{4} - 11 a^{3} + 35 a^{2} + 14 a - 9\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 10 a^{2} - a + 7\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+10a-2\right){x}^{2}+\left(4a^{5}-12a^{4}-11a^{3}+35a^{2}+14a-9\right){x}-a^{5}+3a^{4}+2a^{3}-10a^{2}-a+7$ |
| 27.1-h2 |
27.1-h |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$212.1015630$ |
1.61477 |
\( -39297955917168 a^{5} + 94922885571633 a^{4} + 173379499560459 a^{3} - 291633387290127 a^{2} - 288363429999351 a + 67229573688666 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a - 1\) , \( a^{3} - a^{2} - 2 a\) , \( -3 a^{5} + 14 a^{4} - 10 a^{3} - 26 a^{2} + 32 a - 4\) , \( -14 a^{5} + 50 a^{4} + 3 a^{3} - 111 a^{2} + 31 a - 2\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a-1\right){x}^{2}+\left(-3a^{5}+14a^{4}-10a^{3}-26a^{2}+32a-4\right){x}-14a^{5}+50a^{4}+3a^{3}-111a^{2}+31a-2$ |
| 27.1-i1 |
27.1-i |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.102236323$ |
$6275.451516$ |
3.25632 |
\( -2106 a^{5} + 14985 a^{4} - 32940 a^{3} + 10125 a^{2} + 43254 a - 35397 \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 9 a^{2} - 13 a + 4\) , \( a^{3} - a^{2} - 2 a\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 14 a^{2} + 6 a - 2\) , \( a - 2\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-9a^{2}-13a+4\right){x}^{2}+\left(2a^{5}-6a^{4}-4a^{3}+14a^{2}+6a-2\right){x}+a-2$ |
| 27.1-i2 |
27.1-i |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.034078774$ |
$56479.06364$ |
3.25632 |
\( 31337523 a^{5} - 128952081 a^{4} + 49925556 a^{3} + 257372748 a^{2} - 193378914 a + 28043883 \) |
\( \bigl[a^{4} - 3 a^{3} + 6 a - 3\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 10 a^{2} + 11 a - 5\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 3\) , \( -2 a^{5} + 6 a^{4} + 8 a^{3} - 23 a^{2} - 11 a + 16\) , \( 5 a^{5} - 13 a^{4} - 18 a^{3} + 42 a^{2} + 24 a - 22\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}+6a-3\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-7a^{3}+10a^{2}+11a-5\right){x}^{2}+\left(-2a^{5}+6a^{4}+8a^{3}-23a^{2}-11a+16\right){x}+5a^{5}-13a^{4}-18a^{3}+42a^{2}+24a-22$ |
| 27.1-j1 |
27.1-j |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2287.339174$ |
1.93489 |
\( -607008006 a^{5} + 193715388 a^{4} + 2340294876 a^{3} + 203925438 a^{2} - 1274124573 a + 226434609 \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 4 a + 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 8 a - 1\) , \( -3 a^{4} + a^{3} + 11 a^{2} + 4 a - 1\) , \( -5 a^{5} + 4 a^{4} + 19 a^{3} - 8 a^{2} - 16 a + 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+6a^{2}+8a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-9a^{2}-4a+2\right){x}^{2}+\left(-3a^{4}+a^{3}+11a^{2}+4a-1\right){x}-5a^{5}+4a^{4}+19a^{3}-8a^{2}-16a+3$ |
| 27.1-j2 |
27.1-j |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$20586.05256$ |
1.93489 |
\( -39297955917168 a^{5} + 94922885571633 a^{4} + 173379499560459 a^{3} - 291633387290127 a^{2} - 288363429999351 a + 67229573688666 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( 7 a^{5} - 2 a^{4} - 36 a^{3} - 24 a^{2} + 6 a + 1\) , \( -59 a^{5} + 55 a^{4} + 293 a^{3} + 16 a^{2} - 155 a + 27\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(7a^{5}-2a^{4}-36a^{3}-24a^{2}+6a+1\right){x}-59a^{5}+55a^{4}+293a^{3}+16a^{2}-155a+27$ |
| 27.1-k1 |
27.1-k |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$212.1015630$ |
1.61477 |
\( -20571839670924 a^{5} + 84686501192643 a^{4} - 32847346580697 a^{3} - 169040305433673 a^{2} + 127038715216011 a - 18423269152983 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 2 a^{5} - 3 a^{4} - 5 a^{3} + 7 a^{2} + 3 a - 1\) , \( -3 a^{5} + 3 a^{4} + 10 a^{3} - 4 a^{2} - 4 a + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-5a^{2}-8a+1\right){x}^{2}+\left(2a^{5}-3a^{4}-5a^{3}+7a^{2}+3a-1\right){x}-3a^{5}+3a^{4}+10a^{3}-4a^{2}-4a+1$ |
| 27.1-k2 |
27.1-k |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17180.22660$ |
1.61477 |
\( 8199093861 a^{5} - 22969972953 a^{4} - 29156241303 a^{3} + 76204224981 a^{2} + 39721845717 a - 41310902691 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 9 a^{2} - 12 a + 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 2\) , \( 4 a^{5} - 9 a^{4} - 20 a^{3} + 30 a^{2} + 34 a - 7\) , \( -5 a^{5} + 12 a^{4} + 22 a^{3} - 37 a^{2} - 36 a + 8\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-9a^{2}-12a+3\right){x}^{2}+\left(4a^{5}-9a^{4}-20a^{3}+30a^{2}+34a-7\right){x}-5a^{5}+12a^{4}+22a^{3}-37a^{2}-36a+8$ |
| 27.1-l1 |
27.1-l |
$1$ |
$1$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1525.332737$ |
1.29030 |
\( 1820884570 a^{5} - 1592027539 a^{4} - 9268094856 a^{3} - 623375868 a^{2} + 5249738257 a - 943012354 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{5} - 4 a^{4} + a^{3} + 7 a^{2} - 2 a + 2\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 3 a - 5\) , \( 2 a^{5} + a^{4} - 17 a^{3} + a^{2} + 19 a - 6\) , \( -a^{5} + 7 a^{4} - 5 a^{3} - 12 a^{2} + 16 a - 5\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+3a-5\right){y}={x}^{3}+\left(a^{5}-4a^{4}+a^{3}+7a^{2}-2a+2\right){x}^{2}+\left(2a^{5}+a^{4}-17a^{3}+a^{2}+19a-6\right){x}-a^{5}+7a^{4}-5a^{3}-12a^{2}+16a-5$ |
| 27.1-m1 |
27.1-m |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$20.43143836$ |
1.39994 |
\( 796320068330093137 a^{5} - 2230911883569271789 a^{4} - 2831736699761517383 a^{3} + 7401176184869457587 a^{2} + 3857896101623028994 a - 4012230232721862853 \) |
\( \bigl[a^{4} - 3 a^{3} + 6 a - 3\) , \( a + 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( 72 a^{5} - 207 a^{4} - 214 a^{3} + 627 a^{2} + 284 a - 320\) , \( 454 a^{5} - 1296 a^{4} - 1463 a^{3} + 4088 a^{2} + 1968 a - 2141\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}+6a-3\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(72a^{5}-207a^{4}-214a^{3}+627a^{2}+284a-320\right){x}+454a^{5}-1296a^{4}-1463a^{3}+4088a^{2}+1968a-2141$ |
| 27.1-m2 |
27.1-m |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$14894.51856$ |
1.39994 |
\( 151731 a^{5} - 862353 a^{4} - 214320 a^{3} + 3635577 a^{2} + 1252656 a - 1827213 \) |
\( \bigl[a^{4} - 3 a^{3} + 6 a - 3\) , \( a + 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 9 a - 5\) , \( 3 a^{5} - 3 a^{4} - 9 a^{3} + 5 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}+6a-3\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+9a-5\right){x}+3a^{5}-3a^{4}-9a^{3}+5a^{2}+3a-5$ |
| 27.1-m3 |
27.1-m |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$14894.51856$ |
1.39994 |
\( -4619763599211458927 a^{5} + 4368795675516716792 a^{4} + 22834216279555443787 a^{3} + 711261738874157588 a^{2} - 12398128138840295807 a + 2248798976045317301 \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 6 a^{2} + 3 a\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 10 a - 5\) , \( -62 a^{5} + 238 a^{4} - 48 a^{3} - 493 a^{2} + 272 a - 34\) , \( 422 a^{5} - 1710 a^{4} + 611 a^{3} + 3428 a^{2} - 2482 a + 353\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+3a-1\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+10a-5\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+6a^{2}+3a\right){x}^{2}+\left(-62a^{5}+238a^{4}-48a^{3}-493a^{2}+272a-34\right){x}+422a^{5}-1710a^{4}+611a^{3}+3428a^{2}-2482a+353$ |
| 27.1-n1 |
27.1-n |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$14894.51856$ |
1.39994 |
\( -6771084180533076891 a^{5} + 29803747663716890662 a^{4} - 21460311949981464275 a^{3} - 37631613737255724066 a^{2} + 32432015039181408419 a - 4830894579990068812 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( 88 a^{5} - 247 a^{4} - 295 a^{3} + 791 a^{2} + 390 a - 424\) , \( -462 a^{5} + 1310 a^{4} + 1568 a^{3} - 4227 a^{2} - 2118 a + 2250\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-11a^{2}-11a+8\right){x}^{2}+\left(88a^{5}-247a^{4}-295a^{3}+791a^{2}+390a-424\right){x}-462a^{5}+1310a^{4}+1568a^{3}-4227a^{2}-2118a+2250$ |
| 27.1-n2 |
27.1-n |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$14894.51856$ |
1.39994 |
\( -371835 a^{5} + 1522665 a^{4} - 988206 a^{3} - 1890837 a^{2} + 1592604 a - 238485 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( -2 a^{5} + 8 a^{4} + 5 a^{3} - 24 a^{2} - 10 a + 11\) , \( a^{5} + a^{4} - 3 a^{3} - 8 a^{2} - 2 a + 4\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-11a^{2}-11a+8\right){x}^{2}+\left(-2a^{5}+8a^{4}+5a^{3}-24a^{2}-10a+11\right){x}+a^{5}+a^{4}-3a^{3}-8a^{2}-2a+4$ |
| 27.1-n3 |
27.1-n |
$3$ |
$9$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$20.43143836$ |
1.39994 |
\( -58952752457488515 a^{5} + 18809935951457923 a^{4} + 227290860824076541 a^{3} + 19817440623237963 a^{2} - 123739055493356554 a + 21990202152668141 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( -12 a^{5} + 33 a^{4} + 35 a^{3} - 114 a^{2} - 55 a + 56\) , \( -41 a^{5} + 22 a^{4} + 140 a^{3} - 52 a^{2} - 98 a + 42\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-11a^{2}-11a+8\right){x}^{2}+\left(-12a^{5}+33a^{4}+35a^{3}-114a^{2}-55a+56\right){x}-41a^{5}+22a^{4}+140a^{3}-52a^{2}-98a+42$ |
| 27.1-o1 |
27.1-o |
$1$ |
$1$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1525.332737$ |
1.29030 |
\( 2650612900 a^{5} - 11822464871 a^{4} + 8994313273 a^{3} + 14585431444 a^{2} - 13645170031 a + 2080864404 \) |
\( \bigl[a^{2} - 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 3\) , \( a^{2} - 2\) , \( -3 a^{4} + 13 a^{3} - 4 a^{2} - 23 a + 3\) , \( -5 a^{5} + 18 a^{4} + a^{3} - 33 a^{2} - 4 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+a-3\right){x}^{2}+\left(-3a^{4}+13a^{3}-4a^{2}-23a+3\right){x}-5a^{5}+18a^{4}+a^{3}-33a^{2}-4a+1$ |
| 27.1-p1 |
27.1-p |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.034078774$ |
$56479.06364$ |
3.25632 |
\( 59860377 a^{5} - 144641619 a^{4} - 263914785 a^{3} + 444199410 a^{2} + 438961572 a - 102352338 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 10 a - 1\) , \( a^{3} - a^{2} - 2 a\) , \( 5 a^{5} - 10 a^{4} - 23 a^{3} + 29 a^{2} + 33 a - 7\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 14 a^{2} + 13 a - 3\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+10a-1\right){x}^{2}+\left(5a^{5}-10a^{4}-23a^{3}+29a^{2}+33a-7\right){x}+2a^{5}-4a^{4}-7a^{3}+14a^{2}+13a-3$ |
| 27.1-p2 |
27.1-p |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$139.02525$ |
$(a^3-a^2-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.102236323$ |
$6275.451516$ |
3.25632 |
\( -6399 a^{5} + 10530 a^{4} + 20709 a^{3} - 11178 a^{2} - 1782 a + 1674 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 8 a - 2\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 10 a - 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 3\) , \( 3 a^{5} - 6 a^{4} - 17 a^{3} + 21 a^{2} + 29 a - 6\) , \( 2 a^{5} - 4 a^{4} - 11 a^{3} + 13 a^{2} + 18 a - 4\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+6a^{2}+8a-2\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+8a^{2}+11a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+10a-1\right){x}^{2}+\left(3a^{5}-6a^{4}-17a^{3}+21a^{2}+29a-6\right){x}+2a^{5}-4a^{4}-11a^{3}+13a^{2}+18a-4$ |
| 37.1-a1 |
37.1-a |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$142.72395$ |
$(-a^4+2a^3+3a^2-3a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.072226456$ |
$56104.43117$ |
2.28521 |
\( \frac{262024065}{37} a^{5} - \frac{632903382}{37} a^{4} - \frac{1156055733}{37} a^{3} + \frac{1944483489}{37} a^{2} + \frac{1922787234}{37} a - \frac{448205859}{37} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -4 a^{4} + 8 a^{3} + 9 a^{2} - 12 a + 2\) , \( -2 a^{4} + 3 a^{3} + 6 a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+2\right){x}^{2}+\left(-4a^{4}+8a^{3}+9a^{2}-12a+2\right){x}-2a^{4}+3a^{3}+6a^{2}-4a$ |
| 37.1-a2 |
37.1-a |
$2$ |
$3$ |
6.6.1397493.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{3} \) |
$142.72395$ |
$(-a^4+2a^3+3a^2-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.216679369$ |
$692.6472984$ |
2.28521 |
\( -\frac{13002440326011}{50653} a^{5} + \frac{36425460538638}{50653} a^{4} + \frac{46237058672607}{50653} a^{3} - \frac{120843085936113}{50653} a^{2} - \frac{62990925595713}{50653} a + \frac{65510248079025}{50653} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 4 a^{3} + 9 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 9 a - 2\) , \( -10 a^{5} + 22 a^{4} + 51 a^{3} - 73 a^{2} - 89 a + 22\) , \( -38 a^{5} + 99 a^{4} + 142 a^{3} - 286 a^{2} - 220 a + 54\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+6a^{2}+9a-2\right){y}={x}^{3}+\left(a^{4}-4a^{3}+9a-1\right){x}^{2}+\left(-10a^{5}+22a^{4}+51a^{3}-73a^{2}-89a+22\right){x}-38a^{5}+99a^{4}+142a^{3}-286a^{2}-220a+54$ |
*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.
