| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$4$ |
$33$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$62.23940$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 11$ |
3B, 11B.1.2 |
$14641$ |
\( 1 \) |
$1$ |
$0.030826936$ |
0.647999 |
\( 1606219307040269000685664528235176250888 a^{5} - 505201255314545228245706103526492515760 a^{4} - 7276379701134851706189760667243713057765 a^{3} + 585621608998000505707418880591397665054 a^{2} + 4199487325941333963885321109586284787419 a - 952979041145067887798527201046030804711 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( -a^{5} + 6 a^{3} - 7 a - 2\) , \( a^{2} + a - 1\) , \( -126 a^{5} - 117 a^{4} + 741 a^{3} + 702 a^{2} - 1132 a - 1114\) , \( -3781 a^{5} - 2012 a^{4} + 17879 a^{3} + 9699 a^{2} - 19472 a - 13392\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-7a-2\right){x}^{2}+\left(-126a^{5}-117a^{4}+741a^{3}+702a^{2}-1132a-1114\right){x}-3781a^{5}-2012a^{4}+17879a^{3}+9699a^{2}-19472a-13392$ |
| 1.1-a2 |
1.1-a |
$4$ |
$33$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$62.23940$ |
$\textsf{none}$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 11$ |
3B, 11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$54611.79835$ |
0.647999 |
\( 1214 a^{5} - 2655 a^{4} - 4869 a^{3} + 10240 a^{2} + 3363 a - 5126 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{3} - 4 a - 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 13 a^{2} + 6 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 9 a + 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(2a^{5}-4a^{4}-8a^{3}+13a^{2}+6a-1\right){x}-a^{5}+a^{4}+6a^{3}-4a^{2}-9a+2$ |
| 1.1-a3 |
1.1-a |
$4$ |
$33$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$62.23940$ |
$\textsf{none}$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 11$ |
3B, 11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$54611.79835$ |
0.647999 |
\( 33995809 a^{5} - 134164325 a^{4} + 105734178 a^{3} + 98860224 a^{2} - 110867202 a + 20070137 \) |
\( \bigl[-a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( -3 a^{5} + 3 a^{4} + 14 a^{3} - 10 a^{2} - 12 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 3 a + 3\) , \( -3 a^{5} + 2 a^{4} + 12 a^{3} - 8 a^{2} - 4 a + 10\) , \( 15 a^{5} - 21 a^{4} - 72 a^{3} + 77 a^{2} + 76 a - 28\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-5a+1\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-3a+3\right){y}={x}^{3}+\left(-3a^{5}+3a^{4}+14a^{3}-10a^{2}-12a+3\right){x}^{2}+\left(-3a^{5}+2a^{4}+12a^{3}-8a^{2}-4a+10\right){x}+15a^{5}-21a^{4}-72a^{3}+77a^{2}+76a-28$ |
| 1.1-a4 |
1.1-a |
$4$ |
$33$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$62.23940$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 11$ |
3B, 11B.1.2 |
$14641$ |
\( 1 \) |
$1$ |
$0.030826936$ |
0.647999 |
\( -704508487017687380236064631 a^{5} + 928026387282885932244820277 a^{4} + 3451627389124289054422714003 a^{3} - 3279530943444373844641479073 a^{2} - 3648058152144807590653591164 a + 1031895887258404558223992425 \) |
\( \bigl[a^{3} - 2 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 5 a - 2\) , \( a^{4} - 4 a^{2} + 2\) , \( 12 a^{5} - 309 a^{4} + 430 a^{3} + 744 a^{2} - 744 a - 755\) , \( 246 a^{5} - 5098 a^{4} + 8671 a^{3} + 8475 a^{2} - 12326 a - 7849\bigr] \) |
${y}^2+\left(a^{3}-2a-1\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+5a-2\right){x}^{2}+\left(12a^{5}-309a^{4}+430a^{3}+744a^{2}-744a-755\right){x}+246a^{5}-5098a^{4}+8671a^{3}+8475a^{2}-12326a-7849$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{36} \) |
$74.74559$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$1355.322722$ |
0.972940 |
\( \frac{19534593968251450184}{387420489} a^{5} - \frac{25732253879599264147}{387420489} a^{4} - \frac{95706620059011517651}{387420489} a^{3} + \frac{90934603429118494397}{387420489} a^{2} + \frac{101153218100845110134}{387420489} a - \frac{1059714138202501808}{14348907} \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( a^{5} - 8 a^{4} + 51 a^{3} - 29 a^{2} - 63 a + 5\) , \( 120 a^{5} - 261 a^{4} - 176 a^{3} + 398 a^{2} + 152 a - 73\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-3a+1\right){x}^{2}+\left(a^{5}-8a^{4}+51a^{3}-29a^{2}-63a+5\right){x}+120a^{5}-261a^{4}-176a^{3}+398a^{2}+152a-73$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$74.74559$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$2710.645445$ |
0.972940 |
\( -\frac{220030483}{27} a^{5} + \frac{63276026}{9} a^{4} + \frac{282438134}{9} a^{3} - \frac{54319876}{3} a^{2} - \frac{16907884}{3} a + \frac{53528005}{27} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( 14 a^{5} - 21 a^{4} - 69 a^{3} + 76 a^{2} + 74 a - 27\) , \( 61 a^{5} - 81 a^{4} - 299 a^{3} + 286 a^{2} + 316 a - 92\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+8a-3\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-2\right){x}^{2}+\left(14a^{5}-21a^{4}-69a^{3}+76a^{2}+74a-27\right){x}+61a^{5}-81a^{4}-299a^{3}+286a^{2}+316a-92$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$74.74559$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$2710.645445$ |
0.972940 |
\( -\frac{303931426918868}{19683} a^{5} + \frac{533746013413469}{19683} a^{4} + \frac{1345884677763131}{19683} a^{3} - \frac{2103242860788349}{19683} a^{2} - \frac{1120757691792739}{19683} a + \frac{1246346911943323}{19683} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( 2 a^{5} + 6 a^{4} - 30 a^{3} - 14 a^{2} + 73 a - 17\) , \( -567 a^{5} + 1666 a^{4} + 714 a^{3} - 5224 a^{2} + 3738 a - 617\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(2a^{5}+6a^{4}-30a^{3}-14a^{2}+73a-17\right){x}-567a^{5}+1666a^{4}+714a^{3}-5224a^{2}+3738a-617$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$74.74559$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$1355.322722$ |
0.972940 |
\( \frac{28415401415371915}{729} a^{5} - \frac{83236468416132128}{729} a^{4} - \frac{36313576737257882}{729} a^{3} + \frac{261074947130156095}{729} a^{2} - \frac{185789098122198698}{729} a + \frac{10192405658194375}{243} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( -96 a^{5} + 119 a^{4} + 476 a^{3} - 414 a^{2} - 511 a + 108\) , \( 463 a^{5} - 597 a^{4} - 2282 a^{3} + 2083 a^{2} + 2445 a - 594\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+8a-3\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-2\right){x}^{2}+\left(-96a^{5}+119a^{4}+476a^{3}-414a^{2}-511a+108\right){x}+463a^{5}-597a^{4}-2282a^{3}+2083a^{2}+2445a-594$ |
| 31.1-a1 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$1025.792884$ |
1.47276 |
\( \frac{1147749328284888733960618795900}{29791} a^{5} + \frac{141486795916680191166008423527}{29791} a^{4} - \frac{4290582183397657085249138615742}{29791} a^{3} + \frac{71916226788811881170252052327}{29791} a^{2} + \frac{2448196457529426302571246462997}{29791} a - \frac{540556579537374458371365865485}{29791} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 1\) , \( -11 a^{5} - 5 a^{4} + 48 a^{3} + 67 a^{2} - 90 a - 63\) , \( -337 a^{5} + 1380 a^{4} - 1160 a^{3} - 1156 a^{2} + 1361 a - 13\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(-11a^{5}-5a^{4}+48a^{3}+67a^{2}-90a-63\right){x}-337a^{5}+1380a^{4}-1160a^{3}-1156a^{2}+1361a-13$ |
| 31.1-a2 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{8} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( -\frac{1033073743235841200494976959934}{852891037441} a^{5} + \frac{3933929786659871173277923782815}{852891037441} a^{4} - \frac{2975097977593569902108674723259}{852891037441} a^{3} - \frac{2901568778559675791252921941164}{852891037441} a^{2} + \frac{3183623527721495073846445577852}{852891037441} a - \frac{573680380524522897838041437515}{852891037441} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 3\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( 36 a^{5} + 139 a^{4} - 258 a^{3} - 563 a^{2} + 330 a - 79\) , \( 1873 a^{5} + 784 a^{4} - 9619 a^{3} - 4432 a^{2} + 7810 a - 1392\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-3\right){x}^{2}+\left(36a^{5}+139a^{4}-258a^{3}-563a^{2}+330a-79\right){x}+1873a^{5}+784a^{4}-9619a^{3}-4432a^{2}+7810a-1392$ |
| 31.1-a3 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$8206.343077$ |
1.47276 |
\( \frac{1460546550652965787030}{887503681} a^{5} + \frac{180239481432461299101}{887503681} a^{4} - \frac{5459549052609937959965}{887503681} a^{3} + \frac{91383042197658996772}{887503681} a^{2} + \frac{3115193703304519977774}{887503681} a - \frac{687821042793429817941}{887503681} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 1\) , \( 9 a^{5} - 40 a^{4} + 38 a^{3} + 32 a^{2} - 35 a + 2\) , \( -85 a^{5} + 329 a^{4} - 255 a^{3} - 243 a^{2} + 270 a - 47\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(9a^{5}-40a^{4}+38a^{3}+32a^{2}-35a+2\right){x}-85a^{5}+329a^{4}-255a^{3}-243a^{2}+270a-47$ |
| 31.1-a4 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{24} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( \frac{308629524306573180705764124400765214989728416}{620412660965527688188300451573157121} a^{5} - \frac{96678377635333373686040740401662681795239150}{620412660965527688188300451573157121} a^{4} - \frac{1398478163616726416481971891411691120456947555}{620412660965527688188300451573157121} a^{3} + \frac{111294770463329935355252104822968002094080011}{620412660965527688188300451573157121} a^{2} + \frac{807036468907095340993839638491373208865016181}{620412660965527688188300451573157121} a - \frac{182510843354625433266392408147536567243503960}{620412660965527688188300451573157121} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 6 a^{3} + 7 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a\) , \( -2340 a^{5} + 3083 a^{4} + 11588 a^{3} - 10918 a^{2} - 12508 a + 3176\) , \( -82115 a^{5} + 108051 a^{4} + 403418 a^{3} - 382074 a^{2} - 428431 a + 118082\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-6a^{3}+7a+2\right){x}^{2}+\left(-2340a^{5}+3083a^{4}+11588a^{3}-10918a^{2}-12508a+3176\right){x}-82115a^{5}+108051a^{4}+403418a^{3}-382074a^{2}-428431a+118082$ |
| 31.1-a5 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$65650.74461$ |
1.47276 |
\( \frac{349745746}{31} a^{5} - \frac{614724517}{31} a^{4} - \frac{1548446203}{31} a^{3} + \frac{2422385572}{31} a^{2} + \frac{1289061786}{31} a - \frac{1434751947}{31} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}+{x}$ |
| 31.1-a6 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$65650.74461$ |
1.47276 |
\( -\frac{488148481814}{29791} a^{5} + \frac{1817229407860}{29791} a^{4} - \frac{1334351754367}{29791} a^{3} - \frac{1342176233637}{29791} a^{2} + \frac{1446135272219}{29791} a - \frac{259491223572}{29791} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 6 a^{3} + 7 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a\) , \( -5 a^{5} + 8 a^{4} + 23 a^{3} - 28 a^{2} - 23 a + 11\) , \( 28 a^{5} - 36 a^{4} - 138 a^{3} + 127 a^{2} + 147 a - 39\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-6a^{3}+7a+2\right){x}^{2}+\left(-5a^{5}+8a^{4}+23a^{3}-28a^{2}-23a+11\right){x}+28a^{5}-36a^{4}-138a^{3}+127a^{2}+147a-39$ |
| 31.1-a7 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$8206.343077$ |
1.47276 |
\( -\frac{350193349920473908}{961} a^{5} + \frac{614989688312525919}{961} a^{4} + \frac{1550742937477348718}{961} a^{3} - \frac{2423388078335799313}{961} a^{2} - \frac{1291346530388574699}{961} a + \frac{1436064511168210027}{961} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( -4\) , \( -2 a^{5} + 8 a^{4} + 9 a^{3} - 33 a^{2} - 9 a + 12\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}-4{x}-2a^{5}+8a^{4}+9a^{3}-33a^{2}-9a+12$ |
| 31.1-a8 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$64$ |
\( 2 \) |
$1$ |
$128.2241105$ |
1.47276 |
\( \frac{161977561667364262506242}{923521} a^{5} - \frac{474485436612723225705736}{923521} a^{4} - \frac{206957557465744779382665}{923521} a^{3} + \frac{1488151984849774698530977}{923521} a^{2} - \frac{1059026459496257469864311}{923521} a + \frac{174295328969264546943196}{923521} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( -10 a^{5} + 40 a^{4} + 45 a^{3} - 165 a^{2} - 45 a + 16\) , \( 6 a^{5} + 153 a^{4} - 31 a^{3} - 678 a^{2} - 36 a + 57\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-10a^{5}+40a^{4}+45a^{3}-165a^{2}-45a+16\right){x}+6a^{5}+153a^{4}-31a^{3}-678a^{2}-36a+57$ |
| 31.1-a9 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{12} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$64$ |
\( 2 \) |
$1$ |
$128.2241105$ |
1.47276 |
\( -\frac{1127683403680349712780740748443904004}{787662783788549761} a^{5} + \frac{354688222610355323886840898021118087}{787662783788549761} a^{4} + \frac{5108550614403361265287641142493913090}{787662783788549761} a^{3} - \frac{411149191401225017208777070394047609}{787662783788549761} a^{2} - \frac{2948347178168149967480663778467655563}{787662783788549761} a + \frac{669060970718259450595665810647045219}{787662783788549761} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 1\) , \( 29 a^{5} - 75 a^{4} + 28 a^{3} - 3 a^{2} + 20 a - 13\) , \( 343 a^{5} - 1030 a^{4} + 482 a^{3} + 522 a^{2} - 417 a + 59\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(29a^{5}-75a^{4}+28a^{3}-3a^{2}+20a-13\right){x}+343a^{5}-1030a^{4}+482a^{3}+522a^{2}-417a+59$ |
| 31.1-a10 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$1025.792884$ |
1.47276 |
\( -\frac{11771614728650068311718789996606}{31} a^{5} + \frac{20672646131967906688095174594552}{31} a^{4} + \frac{52127615514169524635482470593815}{31} a^{3} - \frac{81461266340971407505611370906367}{31} a^{2} - \frac{43408078775695757231287999254039}{31} a + \frac{48272736797749486398912337205132}{31} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( 10 a^{5} - 40 a^{4} - 45 a^{3} + 165 a^{2} + 45 a - 104\) , \( -98 a^{5} + 215 a^{4} + 445 a^{3} - 840 a^{2} - 378 a + 495\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}+\left(10a^{5}-40a^{4}-45a^{3}+165a^{2}+45a-104\right){x}-98a^{5}+215a^{4}+445a^{3}-840a^{2}-378a+495$ |
| 31.1-a11 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( \frac{391232997836344118812955063578726935614}{961} a^{5} - \frac{1146049847494581967103997115183815738335}{961} a^{4} - \frac{499875566564262423437058881855118969349}{961} a^{3} + \frac{3594412435730780139116852441515415592364}{961} a^{2} - \frac{2557922789646965076659228190817527550844}{961} a + \frac{420984754490672117422372247124701363035}{961} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( -780 a^{5} + 1038 a^{4} + 3796 a^{3} - 3603 a^{2} - 3947 a + 909\) , \( -18772 a^{5} + 25124 a^{4} + 91377 a^{3} - 88985 a^{2} - 95239 a + 28271\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-2a+3\right){y}={x}^{3}+\left(a^{5}-5a^{3}+5a+1\right){x}^{2}+\left(-780a^{5}+1038a^{4}+3796a^{3}-3603a^{2}-3947a+909\right){x}-18772a^{5}+25124a^{4}+91377a^{3}-88985a^{2}-95239a+28271$ |
| 31.1-a12 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( -\frac{10510572824308508672048934061763533884455273120}{887503681} a^{5} + \frac{3305871471997241704018322895385287159227247726}{887503681} a^{4} + \frac{47614244462683863442287631883194112269531793955}{887503681} a^{3} - \frac{3832115914609593129580786996785582548127284427}{887503681} a^{2} - \frac{27480068985972161720812424402012532444681628853}{887503681} a + \frac{6235982576035498927652588865167121704519444776}{887503681} \) |
\( \bigl[a + 1\) , \( -a^{5} + 5 a^{3} - 3 a + 1\) , \( a^{4} - 3 a^{2} + 1\) , \( -452 a^{5} + 1969 a^{4} - 1949 a^{3} - 1368 a^{2} + 2213 a - 432\) , \( 32265 a^{5} - 121682 a^{4} + 90467 a^{3} + 89084 a^{2} - 96074 a + 17221\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-3a+1\right){x}^{2}+\left(-452a^{5}+1969a^{4}-1949a^{3}-1368a^{2}+2213a-432\right){x}+32265a^{5}-121682a^{4}+90467a^{3}+89084a^{2}-96074a+17221$ |
| 31.1-b1 |
31.1-b |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.011533825$ |
$44479.43355$ |
2.20967 |
\( -\frac{121782753873715}{961} a^{5} + \frac{463527301865015}{961} a^{4} - \frac{349999328708341}{961} a^{3} - \frac{342242022893993}{961} a^{2} + \frac{374527129960401}{961} a - \frac{67437424076363}{961} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( -4 a^{5} - 11 a^{4} + 30 a^{3} + 30 a^{2} - 7 a - 3\) , \( 11 a^{5} + 22 a^{4} - 105 a^{3} - 11 a^{2} + 75 a - 16\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-6a+3\right){y}={x}^{3}+\left(3a^{5}-4a^{4}-13a^{3}+13a^{2}+11a-4\right){x}^{2}+\left(-4a^{5}-11a^{4}+30a^{3}+30a^{2}-7a-3\right){x}+11a^{5}+22a^{4}-105a^{3}-11a^{2}+75a-16$ |
| 31.1-b2 |
31.1-b |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.005766912$ |
$177917.7342$ |
2.20967 |
\( -\frac{1433069}{31} a^{5} + \frac{5349198}{31} a^{4} - \frac{3937183}{31} a^{3} - \frac{3915684}{31} a^{2} + \frac{4225469}{31} a - \frac{762686}{31} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( 11 a^{5} - 11 a^{4} - 50 a^{3} + 35 a^{2} + 43 a - 13\) , \( 5 a^{5} - 4 a^{4} - 24 a^{3} + 15 a^{2} + 21 a - 6\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-6a+3\right){y}={x}^{3}+\left(3a^{5}-4a^{4}-13a^{3}+13a^{2}+11a-4\right){x}^{2}+\left(11a^{5}-11a^{4}-50a^{3}+35a^{2}+43a-13\right){x}+5a^{5}-4a^{4}-24a^{3}+15a^{2}+21a-6$ |
| 41.1-a1 |
41.1-a |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$84.81331$ |
$(a^5-5a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.017230132$ |
$32440.58324$ |
2.40753 |
\( -\frac{14540938647674287}{1681} a^{5} + \frac{55342741171488873}{1681} a^{4} - \frac{41785489535847104}{1681} a^{3} - \frac{40862008511943361}{1681} a^{2} + \frac{44715082991653178}{1681} a - \frac{8051386985634292}{1681} \) |
\( \bigl[-a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 4 a\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 14 a^{2} - 9 a + 6\) , \( a^{2} + a - 2\) , \( -a^{4} + 3 a^{3} - 4 a^{2} - 3 a + 3\) , \( -4 a^{5} + 6 a^{4} + 11 a^{3} - 12 a^{2} - 10 a + 3\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-4a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-3a^{5}+4a^{4}+13a^{3}-14a^{2}-9a+6\right){x}^{2}+\left(-a^{4}+3a^{3}-4a^{2}-3a+3\right){x}-4a^{5}+6a^{4}+11a^{3}-12a^{2}-10a+3$ |
| 41.1-a2 |
41.1-a |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$84.81331$ |
$(a^5-5a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008615066$ |
$129762.3329$ |
2.40753 |
\( \frac{16004449}{41} a^{5} - \frac{59242798}{41} a^{4} + \frac{41300145}{41} a^{3} + \frac{45535311}{41} a^{2} - \frac{44435116}{41} a + \frac{7725820}{41} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + a + 5\) , \( 1\) , \( -a^{5} + 4 a^{4} + 2 a^{3} - 14 a^{2} - a + 10\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 13 a^{2} - 5 a + 8\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-7a^{2}+a+5\right){x}^{2}+\left(-a^{5}+4a^{4}+2a^{3}-14a^{2}-a+10\right){x}-2a^{5}+4a^{4}+7a^{3}-13a^{2}-5a+8$ |
| 41.1-b1 |
41.1-b |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$84.81331$ |
$(a^5-5a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.013367346$ |
$77513.07453$ |
2.23144 |
\( \frac{294168139}{41} a^{5} - \frac{516515752}{41} a^{4} - \frac{1302673384}{41} a^{3} + \frac{2035316193}{41} a^{2} + \frac{1084801605}{41} a - \frac{1206034084}{41} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 5 a + 2\) , \( a^{3} - 2 a - 1\) , \( -2 a^{5} + 3 a^{4} + 7 a^{3} - 4 a^{2} - 8 a + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 5 a^{2} - a\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-5a+2\right){x}^{2}+\left(-2a^{5}+3a^{4}+7a^{3}-4a^{2}-8a+3\right){x}-a^{5}+3a^{4}+2a^{3}-5a^{2}-a$ |
| 41.1-b2 |
41.1-b |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$84.81331$ |
$(a^5-5a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.004455782$ |
$77513.07453$ |
2.23144 |
\( \frac{57994411213}{68921} a^{5} - \frac{36997763035}{68921} a^{4} - \frac{348580821866}{68921} a^{3} + \frac{155415303320}{68921} a^{2} + \frac{514326915814}{68921} a - \frac{129528231830}{68921} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 7 a + 2\) , \( a^{5} - 5 a^{3} + 5 a\) , \( -2 a^{5} + a^{4} + 9 a^{3} - a^{2} - 9 a - 2\) , \( -44 a^{5} + 82 a^{4} + 189 a^{3} - 329 a^{2} - 145 a + 209\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-7a+2\right){x}^{2}+\left(-2a^{5}+a^{4}+9a^{3}-a^{2}-9a-2\right){x}-44a^{5}+82a^{4}+189a^{3}-329a^{2}-145a+209$ |
| 41.1-b3 |
41.1-b |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{6} \) |
$84.81331$ |
$(a^5-5a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.008911564$ |
$19378.26863$ |
2.23144 |
\( \frac{5160746097604466171083}{4750104241} a^{5} - \frac{15116996144924874322550}{4750104241} a^{4} - \frac{6596324090888058193728}{4750104241} a^{3} + \frac{47417622246192743893408}{4750104241} a^{2} - \frac{33743571908962038596076}{4750104241} a + \frac{5553513136786228568492}{4750104241} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( 7 a^{5} + a^{4} - 46 a^{3} + 59 a - 26\) , \( 18 a^{5} - 20 a^{4} - 50 a^{3} + 53 a^{2} - 44 a + 23\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-3a+2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-2a+3\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){x}^{2}+\left(7a^{5}+a^{4}-46a^{3}+59a-26\right){x}+18a^{5}-20a^{4}-50a^{3}+53a^{2}-44a+23$ |
| 41.1-b4 |
41.1-b |
$4$ |
$6$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$84.81331$ |
$(a^5-5a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.026734693$ |
$19378.26863$ |
2.23144 |
\( -\frac{247312191821393399}{1681} a^{5} + \frac{434315726526349312}{1681} a^{4} + \frac{1095159425055437131}{1681} a^{3} - \frac{1711435916724291643}{1681} a^{2} - \frac{911968936218596275}{1681} a + \frac{1014171519640582545}{1681} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 5 a + 2\) , \( a^{3} - 2 a - 1\) , \( -22 a^{5} + 28 a^{4} + 107 a^{3} - 89 a^{2} - 118 a + 18\) , \( -82 a^{5} + 112 a^{4} + 399 a^{3} - 397 a^{2} - 420 a + 138\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-5a+2\right){x}^{2}+\left(-22a^{5}+28a^{4}+107a^{3}-89a^{2}-118a+18\right){x}-82a^{5}+112a^{4}+399a^{3}-397a^{2}-420a+138$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$4658.728355$ |
1.67217 |
\( \frac{1287545907}{7} a^{5} - \frac{1693566461}{7} a^{4} - \frac{6310424038}{7} a^{3} + \frac{5984983744}{7} a^{2} + \frac{6664599078}{7} a - \frac{1884723034}{7} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 3 a + 3\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a + 2\) , \( 4 a^{5} - 8 a^{4} - 16 a^{3} + 32 a^{2} + 10 a - 24\) , \( -21 a^{5} + 37 a^{4} + 92 a^{3} - 148 a^{2} - 74 a + 90\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-3a+3\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){x}^{2}+\left(4a^{5}-8a^{4}-16a^{3}+32a^{2}+10a-24\right){x}-21a^{5}+37a^{4}+92a^{3}-148a^{2}-74a+90$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{4} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2329.364177$ |
1.67217 |
\( -\frac{44682954498275}{49} a^{5} + \frac{20731677864676}{49} a^{4} + \frac{214541279828608}{49} a^{3} - \frac{20858262562702}{49} a^{2} - \frac{124233907036096}{49} a + \frac{28389749219352}{49} \) |
\( \bigl[a^{2} + a - 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 10 a^{2} + 6 a - 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 3 a + 4\) , \( -6 a^{5} + 2 a^{4} + 42 a^{3} + 5 a^{2} - 71 a - 40\) , \( 11 a^{5} + 11 a^{4} - 89 a^{3} - 91 a^{2} + 157 a + 153\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-3a+4\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-8a^{3}+10a^{2}+6a-3\right){x}^{2}+\left(-6a^{5}+2a^{4}+42a^{3}+5a^{2}-71a-40\right){x}+11a^{5}+11a^{4}-89a^{3}-91a^{2}+157a+153$ |
| 49.1-b1 |
49.1-b |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$787.0481287$ |
1.12999 |
\( \frac{30176477175473918504}{49} a^{5} - \frac{370959595583589700360}{343} a^{4} - \frac{935402224099909297679}{343} a^{3} + \frac{1461778923930007873681}{343} a^{2} + \frac{778934793586578494395}{343} a - \frac{866228484050474713990}{343} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( a^{5} - 4 a^{4} - 8 a^{3} + 14 a^{2} + 9 a - 10\) , \( 6 a^{5} - 4 a^{4} - 24 a^{3} + 17 a^{2} + 13 a - 14\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-2a+3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-1\right){x}^{2}+\left(a^{5}-4a^{4}-8a^{3}+14a^{2}+9a-10\right){x}+6a^{5}-4a^{4}-24a^{3}+17a^{2}+13a-14$ |
| 49.1-b2 |
49.1-b |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$787.0481287$ |
1.12999 |
\( -\frac{33421578235106}{7} a^{5} + \frac{44025168524177}{7} a^{4} + \frac{163743713309159}{7} a^{3} - \frac{155579519258196}{7} a^{2} - \frac{173062304078080}{7} a + \frac{48952686264565}{7} \) |
\( \bigl[a^{4} - 3 a^{2} - a + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + a + 4\) , \( a^{5} - 5 a^{3} + 4 a\) , \( a^{5} - 5 a^{4} - 6 a^{3} + 16 a^{2} + 3 a - 5\) , \( -17 a^{5} - 12 a^{4} + 59 a^{3} + 37 a^{2} - 26 a - 15\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}-a+1\right){x}{y}+\left(a^{5}-5a^{3}+4a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-7a^{2}+a+4\right){x}^{2}+\left(a^{5}-5a^{4}-6a^{3}+16a^{2}+3a-5\right){x}-17a^{5}-12a^{4}+59a^{3}+37a^{2}-26a-15$ |
| 49.1-c1 |
49.1-c |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{10} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$4621.469872$ |
1.65880 |
\( \frac{795540805}{16807} a^{5} - \frac{1001826365}{16807} a^{4} - \frac{4000609051}{16807} a^{3} + \frac{3577994149}{16807} a^{2} + \frac{4448111321}{16807} a - \frac{1220726677}{16807} \) |
\( \bigl[-a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 5\) , \( a^{5} - 5 a^{3} + 4 a + 1\) , \( 4 a^{5} - 7 a^{4} - 19 a^{3} + 24 a^{2} + 23 a - 7\) , \( 3 a^{5} - 3 a^{4} - 15 a^{3} + 11 a^{2} + 14 a - 5\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-6a+3\right){x}{y}+\left(a^{5}-5a^{3}+4a+1\right){y}={x}^{3}+\left(3a^{5}-4a^{4}-13a^{3}+13a^{2}+11a-5\right){x}^{2}+\left(4a^{5}-7a^{4}-19a^{3}+24a^{2}+23a-7\right){x}+3a^{5}-3a^{4}-15a^{3}+11a^{2}+14a-5$ |
| 49.1-c2 |
49.1-c |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{20} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2310.734936$ |
1.65880 |
\( \frac{10036119836964947}{282475249} a^{5} - \frac{29399419342483055}{282475249} a^{4} - \frac{12822844127834407}{282475249} a^{3} + \frac{92208680747113198}{282475249} a^{2} - \frac{65621823291227116}{282475249} a + \frac{10801128327256298}{282475249} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( a^{4} - 4 a^{2} - a + 2\) , \( 13 a^{5} - 4 a^{4} - 57 a^{3} + 5 a^{2} + 28 a - 11\) , \( 23 a^{5} - 35 a^{4} - 114 a^{3} + 128 a^{2} + 130 a - 40\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-7a+3\right){x}{y}+\left(a^{4}-4a^{2}-a+2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-5a+1\right){x}^{2}+\left(13a^{5}-4a^{4}-57a^{3}+5a^{2}+28a-11\right){x}+23a^{5}-35a^{4}-114a^{3}+128a^{2}+130a-40$ |
| 49.1-d1 |
49.1-d |
$1$ |
$1$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.008207757$ |
$36705.14889$ |
2.59523 |
\( -\frac{6613630491}{7} a^{5} + \frac{8709281037}{7} a^{4} + \frac{32409828699}{7} a^{3} - \frac{30787577825}{7} a^{2} - \frac{34253730020}{7} a + \frac{9688739659}{7} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a + 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 10 a^{2} - 5 a + 4\) , \( a^{5} - 5 a^{3} + 4 a\) , \( -13 a^{5} + 21 a^{4} + 55 a^{3} - 79 a^{2} - 41 a + 43\) , \( -20 a^{5} + 30 a^{4} + 84 a^{3} - 118 a^{2} - 64 a + 68\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a+2\right){x}{y}+\left(a^{5}-5a^{3}+4a\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-10a^{2}-5a+4\right){x}^{2}+\left(-13a^{5}+21a^{4}+55a^{3}-79a^{2}-41a+43\right){x}-20a^{5}+30a^{4}+84a^{3}-118a^{2}-64a+68$ |
| 49.1-e1 |
49.1-e |
$4$ |
$15$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$25851.83438$ |
1.48465 |
\( \frac{10519949743062}{343} a^{5} + \frac{1296848109034}{343} a^{4} - \frac{39326262085697}{343} a^{3} + \frac{659101502840}{343} a^{2} + \frac{22439443726594}{343} a - \frac{4954576885729}{343} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( -a^{4} + 3 a^{2} + 2 a\) , \( a^{3} - 3 a - 1\) , \( a^{5} - 2 a^{4} - 8 a^{3} + 8 a^{2} + 15 a + 2\) , \( 7 a^{5} - 19 a^{4} - 15 a^{3} + 62 a^{2} - 24 a - 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-1\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{4}+3a^{2}+2a\right){x}^{2}+\left(a^{5}-2a^{4}-8a^{3}+8a^{2}+15a+2\right){x}+7a^{5}-19a^{4}-15a^{3}+62a^{2}-24a-2$ |
| 49.1-e2 |
49.1-e |
$4$ |
$15$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$25851.83438$ |
1.48465 |
\( -93453430 a^{5} + \frac{205748003}{7} a^{4} + \frac{2963501531}{7} a^{3} - \frac{238478155}{7} a^{2} - \frac{1710346227}{7} a + \frac{388114192}{7} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 3 a - 2\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 4 a\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a + 1\) , \( -5 a^{5} + 14 a^{4} + 8 a^{3} - 44 a^{2} + 28 a - 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-4a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-3a-2\right){x}^{2}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a+1\right){x}-5a^{5}+14a^{4}+8a^{3}-44a^{2}+28a-5$ |
| 49.1-e3 |
49.1-e |
$4$ |
$15$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{30} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.4[2] |
$625$ |
\( 1 \) |
$1$ |
$1.654517400$ |
1.48465 |
\( -\frac{5071828648518898928776706}{4747561509943} a^{5} + \frac{1594371267260221471874998}{4747561509943} a^{4} + \frac{22976097914409962241364493}{4747561509943} a^{3} - \frac{1845254644248882604992608}{4747561509943} a^{2} - \frac{13259741923351079752225853}{4747561509943} a + \frac{3007050597491418428537932}{4747561509943} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 2\) , \( a^{4} - 4 a^{2} + 2\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 3\) , \( 1286 a^{5} - 1768 a^{4} - 6218 a^{3} + 6370 a^{2} + 6394 a - 2350\) , \( -41543 a^{5} + 53994 a^{4} + 204324 a^{3} - 189619 a^{2} - 217635 a + 56419\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+2\right){x}{y}+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-7a+3\right){y}={x}^{3}+\left(a^{4}-4a^{2}+2\right){x}^{2}+\left(1286a^{5}-1768a^{4}-6218a^{3}+6370a^{2}+6394a-2350\right){x}-41543a^{5}+53994a^{4}+204324a^{3}-189619a^{2}-217635a+56419$ |
| 49.1-e4 |
49.1-e |
$4$ |
$15$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{10} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.4[2] |
$625$ |
\( 1 \) |
$1$ |
$1.654517400$ |
1.48465 |
\( \frac{1868725201871035180068}{2401} a^{5} - \frac{49786647890889419082432}{16807} a^{4} + \frac{37590650528569269107756}{16807} a^{3} + \frac{36759694234274090980991}{16807} a^{2} - \frac{40226057957192491342390}{16807} a + \frac{7243098992357634858294}{16807} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 7 a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( -67 a^{5} + 147 a^{4} + 136 a^{3} - 479 a^{2} + 248 a - 44\) , \( -611 a^{5} + 1384 a^{4} + 1064 a^{3} - 4447 a^{2} + 2879 a - 492\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-7a+1\right){x}^{2}+\left(-67a^{5}+147a^{4}+136a^{3}-479a^{2}+248a-44\right){x}-611a^{5}+1384a^{4}+1064a^{3}-4447a^{2}+2879a-492$ |
| 49.1-f1 |
49.1-f |
$1$ |
$1$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.006790174$ |
$41021.07672$ |
2.39946 |
\( -\frac{5980179215}{7} a^{5} + \frac{700090460}{7} a^{4} + \frac{21196892310}{7} a^{3} - 667291825 a^{2} - 1239034905 a + \frac{2088108851}{7} \) |
\( \bigl[a + 1\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 14 a^{2} - 9 a + 5\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( -4 a^{5} + 2 a^{4} + 20 a^{3} - 6 a^{2} - 21 a + 3\) , \( -3 a^{5} + 3 a^{4} + 14 a^{3} - 10 a^{2} - 13 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+8a-3\right){y}={x}^{3}+\left(-3a^{5}+4a^{4}+13a^{3}-14a^{2}-9a+5\right){x}^{2}+\left(-4a^{5}+2a^{4}+20a^{3}-6a^{2}-21a+3\right){x}-3a^{5}+3a^{4}+14a^{3}-10a^{2}-13a+1$ |
| 49.1-g1 |
49.1-g |
$1$ |
$1$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{10} \) |
$86.08254$ |
$(-2a^5+3a^4+10a^3-12a^2-11a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.002309606$ |
$25038.61395$ |
2.49082 |
\( -\frac{9279771421}{16807} a^{5} + \frac{4802428873}{16807} a^{4} + \frac{42736263636}{16807} a^{3} - \frac{11435831123}{16807} a^{2} - \frac{29084734183}{16807} a + \frac{7143586071}{16807} \) |
\( \bigl[a + 1\) , \( -2 a^{5} + 2 a^{4} + 10 a^{3} - 7 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 2\) , \( -2 a^{5} + 2 a^{4} + 8 a^{3} - 4 a^{2} - 7 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 2 a^{2} + 6 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-2\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+10a^{3}-7a^{2}-9a+2\right){x}^{2}+\left(-2a^{5}+2a^{4}+8a^{3}-4a^{2}-7a+1\right){x}+a^{5}-2a^{4}-3a^{3}+2a^{2}+6a+3$ |
| 59.2-a1 |
59.2-a |
$1$ |
$1$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
59.2 |
\( 59 \) |
\( -59 \) |
$87.42515$ |
$(-a^4+a^3+3a^2-3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.011019161$ |
$25511.37894$ |
2.42163 |
\( \frac{11048}{59} a^{5} - \frac{11375}{59} a^{4} - \frac{30730}{59} a^{3} + \frac{29362}{59} a^{2} - \frac{55427}{59} a + \frac{52669}{59} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a + 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 11 a^{2} - 6 a + 7\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( -6 a^{5} + 11 a^{4} + 24 a^{3} - 39 a^{2} - 19 a + 22\) , \( -4 a^{5} + 8 a^{4} + 15 a^{3} - 27 a^{2} - 12 a + 15\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a+2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-11a^{2}-6a+7\right){x}^{2}+\left(-6a^{5}+11a^{4}+24a^{3}-39a^{2}-19a+22\right){x}-4a^{5}+8a^{4}+15a^{3}-27a^{2}-12a+15$ |
| 59.3-a1 |
59.3-a |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59 \) |
$87.42515$ |
$(a^5-a^4-4a^3+4a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$1217.389386$ |
1.74784 |
\( \frac{4359301206760773428367717}{59} a^{5} + \frac{537385250403166009110948}{59} a^{4} - \frac{16296189097092649182107067}{59} a^{3} + \frac{273147181618590226616345}{59} a^{2} + \frac{9298568519001795165747303}{59} a - \frac{2053104185232518599834604}{59} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 13 a^{2} - 10 a + 5\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 1\) , \( -11 a^{5} + 3 a^{4} + 46 a^{3} - 15 a^{2} - 27 a + 7\) , \( 6 a^{5} - 4 a^{4} + 8 a^{3} + 8 a^{2} - 15 a + 2\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-3a+1\right){y}={x}^{3}+\left(-3a^{5}+4a^{4}+13a^{3}-13a^{2}-10a+5\right){x}^{2}+\left(-11a^{5}+3a^{4}+46a^{3}-15a^{2}-27a+7\right){x}+6a^{5}-4a^{4}+8a^{3}+8a^{2}-15a+2$ |
| 59.3-a2 |
59.3-a |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59^{3} \) |
$87.42515$ |
$(a^5-a^4-4a^3+4a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$1217.389386$ |
1.74784 |
\( \frac{405899147170}{205379} a^{5} - \frac{12701658626728}{205379} a^{4} + \frac{44961131124416}{205379} a^{3} - \frac{16357875028693}{205379} a^{2} - \frac{50805246375551}{205379} a + \frac{12754961594912}{205379} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 2\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 3\) , \( 13 a^{5} - 5 a^{4} - 54 a^{3} + 11 a^{2} + 26 a - 8\) , \( -19 a^{5} + 6 a^{4} + 95 a^{3} - 8 a^{2} - 61 a + 14\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+2\right){x}{y}+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-7a+3\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-2\right){x}^{2}+\left(13a^{5}-5a^{4}-54a^{3}+11a^{2}+26a-8\right){x}-19a^{5}+6a^{4}+95a^{3}-8a^{2}-61a+14$ |
| 59.3-b1 |
59.3-b |
$1$ |
$1$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59 \) |
$87.42515$ |
$(a^5-a^4-4a^3+4a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.001630970$ |
$164018.2308$ |
2.30442 |
\( \frac{1370532}{59} a^{5} + \frac{445702}{59} a^{4} - \frac{5167788}{59} a^{3} - \frac{815081}{59} a^{2} + \frac{3174888}{59} a - \frac{498817}{59} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( -a + 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 4\) , \( -a^{5} + 6 a^{3} - 2 a^{2} - 6 a + 3\) , \( a^{4} - 2 a^{3} - a^{2} + a - 1\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-2\right){x}{y}+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-7a+4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{5}+6a^{3}-2a^{2}-6a+3\right){x}+a^{4}-2a^{3}-a^{2}+a-1$ |
| 59.3-c1 |
59.3-c |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59^{3} \) |
$87.42515$ |
$(a^5-a^4-4a^3+4a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.001554253$ |
$64625.94913$ |
2.59582 |
\( \frac{818400094322}{205379} a^{5} + \frac{129154928059}{205379} a^{4} - \frac{3025464415724}{205379} a^{3} - \frac{50369969932}{205379} a^{2} + \frac{1670933038974}{205379} a - \frac{361031104784}{205379} \) |
\( \bigl[a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 4\) , \( -a^{3} + 2 a - 1\) , \( -a^{2} - a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-7a+4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(-a^{3}+2a-1\right){x}-a^{2}-a+1$ |
| 59.3-c2 |
59.3-c |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59 \) |
$87.42515$ |
$(a^5-a^4-4a^3+4a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.004662761$ |
$64625.94913$ |
2.59582 |
\( -\frac{64159824}{59} a^{5} + \frac{113765350}{59} a^{4} + \frac{284040300}{59} a^{3} - \frac{448947221}{59} a^{2} - \frac{237393187}{59} a + \frac{265776207}{59} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} - 3 a + 5\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 5 a + 3\) , \( -4 a^{5} + 3 a^{4} + 16 a^{3} - 13 a^{2} - 11 a + 9\) , \( -4 a^{5} + 2 a^{4} + 16 a^{3} - 9 a^{2} - 11 a + 6\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-5a+3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-8a^{2}-3a+5\right){x}^{2}+\left(-4a^{5}+3a^{4}+16a^{3}-13a^{2}-11a+9\right){x}-4a^{5}+2a^{4}+16a^{3}-9a^{2}-11a+6$ |
| 64.1-a1 |
64.1-a |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{6} \) |
$88.01980$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.023351260$ |
$13990.33726$ |
2.81425 |
\( -\frac{11449}{2} a^{5} + \frac{41601}{2} a^{4} - 12323 a^{3} - \frac{41173}{2} a^{2} + \frac{35495}{2} a - 2524 \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{5} + 5 a^{3} - 5 a\) , \( a^{2} - 1\) , \( a^{5} - 3 a^{3} - a^{2} + 2 a + 1\) , \( 2 a^{5} - 7 a^{3} + 4 a - 1\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-5a\right){x}^{2}+\left(a^{5}-3a^{3}-a^{2}+2a+1\right){x}+2a^{5}-7a^{3}+4a-1$ |
| 64.1-a2 |
64.1-a |
$2$ |
$3$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{18} \) |
$88.01980$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.007783753$ |
$13990.33726$ |
2.81425 |
\( -\frac{372514795}{2} a^{5} + \frac{1962808611}{8} a^{4} + \frac{3650149817}{4} a^{3} - \frac{6936306195}{8} a^{2} - \frac{7715765979}{8} a + \frac{2182489307}{8} \) |
\( \bigl[a^{4} - 3 a^{2} - a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + a + 1\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 2\) , \( -4 a^{4} + 16 a^{2} + a - 5\) , \( 4 a^{5} - 5 a^{4} - 17 a^{3} + 18 a^{2} + 9 a - 12\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}-a+1\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+8a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+a+1\right){x}^{2}+\left(-4a^{4}+16a^{2}+a-5\right){x}+4a^{5}-5a^{4}-17a^{3}+18a^{2}+9a-12$ |
| 64.1-b1 |
64.1-b |
$2$ |
$7$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{42} \) |
$88.01980$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1.423093751$ |
$0.607208088$ |
2.55323 |
\( -\frac{661423578612904638319}{64} a^{5} + \frac{2517381707375973330273}{64} a^{4} - \frac{950355314310097681067}{32} a^{3} - \frac{3717389947572253097155}{128} a^{2} + \frac{4067931975116471451485}{128} a - \frac{366235659528699810345}{64} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 3 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 4\) , \( -98 a^{5} + 20 a^{4} + 286 a^{3} - 83 a^{2} + 45 a - 74\) , \( -14247 a^{5} - 1644 a^{4} + 52563 a^{3} - 926 a^{2} - 28214 a + 5435\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+3\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-2a+4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+3a-2\right){x}^{2}+\left(-98a^{5}+20a^{4}+286a^{3}-83a^{2}+45a-74\right){x}-14247a^{5}-1644a^{4}+52563a^{3}-926a^{2}-28214a+5435$ |
*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.
