| 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 |
| 41.1-a1 |
41.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$651.9024896$ |
2.27600 |
\( -\frac{8984179006241268697160}{41} a^{5} - \frac{4444553688617899720556}{41} a^{4} + \frac{56245938903177637867836}{41} a^{3} + \frac{21182054771657449538079}{41} a^{2} - \frac{76149141402730689873442}{41} a - \frac{6010654485773269437037}{41} \) |
\( \bigl[a\) , \( -a^{5} - a^{4} + 7 a^{3} + 6 a^{2} - 11 a - 6\) , \( a^{5} - 6 a^{3} + 8 a\) , \( 63 a^{5} - 6 a^{4} - 373 a^{3} + 173 a^{2} + 561 a - 419\) , \( 374 a^{5} - 88 a^{4} - 2271 a^{3} + 1296 a^{2} + 3479 a - 2865\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}+8a\right){y}={x}^{3}+\left(-a^{5}-a^{4}+7a^{3}+6a^{2}-11a-6\right){x}^{2}+\left(63a^{5}-6a^{4}-373a^{3}+173a^{2}+561a-419\right){x}+374a^{5}-88a^{4}-2271a^{3}+1296a^{2}+3479a-2865$ |
| 41.1-a2 |
41.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$20860.87966$ |
2.27600 |
\( -\frac{14597338066672}{1681} a^{5} - \frac{7221408650287}{1681} a^{4} + \frac{91387418873252}{1681} a^{3} + \frac{34416098786654}{1681} a^{2} - \frac{123725798041612}{1681} a - \frac{9765838570959}{1681} \) |
\( \bigl[a\) , \( -a^{5} - a^{4} + 7 a^{3} + 6 a^{2} - 11 a - 6\) , \( a^{5} - 6 a^{3} + 8 a\) , \( -7 a^{5} - 11 a^{4} + 32 a^{3} + 38 a^{2} - 39 a - 24\) , \( 7 a^{5} + 5 a^{4} - 36 a^{3} - 8 a^{2} + 49 a - 12\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}+8a\right){y}={x}^{3}+\left(-a^{5}-a^{4}+7a^{3}+6a^{2}-11a-6\right){x}^{2}+\left(-7a^{5}-11a^{4}+32a^{3}+38a^{2}-39a-24\right){x}+7a^{5}+5a^{4}-36a^{3}-8a^{2}+49a-12$ |
| 41.1-a3 |
41.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$10430.43983$ |
2.27600 |
\( \frac{1260951708}{41} a^{5} + \frac{269913471}{41} a^{4} - \frac{8498646764}{41} a^{3} - \frac{1490592607}{41} a^{2} + \frac{13320684705}{41} a + \frac{1038742621}{41} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 8 a - 3\) , \( 2 a^{5} + a^{4} - 14 a^{3} - 4 a^{2} + 22 a\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a + 1\) , \( -2 a^{3} + 5 a\) , \( -3 a^{5} + 6 a^{4} + 7 a^{3} - 17 a^{2} + 4 a\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+8a-3\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a+1\right){y}={x}^{3}+\left(2a^{5}+a^{4}-14a^{3}-4a^{2}+22a\right){x}^{2}+\left(-2a^{3}+5a\right){x}-3a^{5}+6a^{4}+7a^{3}-17a^{2}+4a$ |
| 41.1-a4 |
41.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$20860.87966$ |
2.27600 |
\( -\frac{168461786556360}{2825761} a^{5} + \frac{511716866081588}{2825761} a^{4} + \frac{138562484540900}{2825761} a^{3} - \frac{1462387435858103}{2825761} a^{2} + \frac{953194658002650}{2825761} a + \frac{82830457729933}{2825761} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 6 a^{2} + 29 a + 5\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 2\) , \( 2 a^{5} - 9 a^{4} + 3 a^{3} + 23 a^{2} - 26 a + 3\) , \( -22 a^{5} + 24 a^{4} + 95 a^{3} - 62 a^{2} - 87 a - 7\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+2\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-2\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}-6a^{2}+29a+5\right){x}^{2}+\left(2a^{5}-9a^{4}+3a^{3}+23a^{2}-26a+3\right){x}-22a^{5}+24a^{4}+95a^{3}-62a^{2}-87a-7$ |
| 41.1-a5 |
41.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{8} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1303.804979$ |
2.27600 |
\( \frac{885542140797128688333102}{7984925229121} a^{5} + \frac{955794109593857013122388}{7984925229121} a^{4} - \frac{4203761130028915963020406}{7984925229121} a^{3} - \frac{2546762038792787355090604}{7984925229121} a^{2} + \frac{5302368119779655229510389}{7984925229121} a + \frac{424835420971664723996149}{7984925229121} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 6 a^{2} + 29 a + 5\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 2\) , \( 12 a^{5} - 4 a^{4} - 72 a^{3} - 2 a^{2} + 109 a + 13\) , \( -22 a^{5} + 37 a^{4} + 82 a^{3} - 116 a^{2} - 34 a - 3\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+2\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-2\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}-6a^{2}+29a+5\right){x}^{2}+\left(12a^{5}-4a^{4}-72a^{3}-2a^{2}+109a+13\right){x}-22a^{5}+37a^{4}+82a^{3}-116a^{2}-34a-3$ |
| 41.1-a6 |
41.1-a |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5215.219916$ |
2.27600 |
\( -\frac{197905866363742218686}{1681} a^{5} + \frac{600671715893159422284}{1681} a^{4} + \frac{162890925250602345366}{1681} a^{3} - \frac{1716846659406171103780}{1681} a^{2} + \frac{1119150351391201832075}{1681} a + \frac{97244421297428052459}{1681} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 4 a^{2} + 29 a - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 8 a - 3\) , \( -a^{4} + 5 a^{3} - a^{2} - 17 a + 6\) , \( -27 a^{5} - 8 a^{4} + 166 a^{3} + 45 a^{2} - 223 a - 23\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+8a-3\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}-4a^{2}+29a-2\right){x}^{2}+\left(-a^{4}+5a^{3}-a^{2}-17a+6\right){x}-27a^{5}-8a^{4}+166a^{3}+45a^{2}-223a-23$ |
| 41.1-b1 |
41.1-b |
$2$ |
$7$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$42113.16227$ |
1.50031 |
\( -\frac{1669545727}{1681} a^{5} - \frac{356208233}{1681} a^{4} + \frac{11254384379}{1681} a^{3} + \frac{1969603507}{1681} a^{2} - \frac{17644006659}{1681} a - \frac{1376569651}{1681} \) |
\( \bigl[-a^{5} + 7 a^{3} + a^{2} - 10 a - 1\) , \( -a^{4} + 6 a^{2} - a - 6\) , \( a^{2} - 2\) , \( 3 a^{3} + 4 a^{2} - 8 a - 2\) , \( 2 a^{5} + 8 a^{4} - 6 a^{3} - 43 a^{2} - 3 a + 55\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+a^{2}-10a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-a-6\right){x}^{2}+\left(3a^{3}+4a^{2}-8a-2\right){x}+2a^{5}+8a^{4}-6a^{3}-43a^{2}-3a+55$ |
| 41.1-b2 |
41.1-b |
$2$ |
$7$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{14} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 2 \) |
$1$ |
$0.357955973$ |
1.50031 |
\( \frac{3994507357674741603296625125869374470}{37929227194915558802161} a^{5} + \frac{1976118326644757612365959956611161273}{37929227194915558802161} a^{4} - \frac{25007829804251700012032562188202123255}{37929227194915558802161} a^{3} - \frac{9417874613411500255981970467083831998}{37929227194915558802161} a^{2} + \frac{33857106961303163824780707970707024449}{37929227194915558802161} a + \frac{2672431597592452105549243894349194373}{37929227194915558802161} \) |
\( \bigl[a^{2} + a - 3\) , \( 2 a^{5} + a^{4} - 14 a^{3} - 5 a^{2} + 21 a + 1\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 3\) , \( 102 a^{5} - 76 a^{4} - 608 a^{3} + 158 a^{2} + 848 a + 37\) , \( -2535 a^{5} - 1587 a^{4} + 18360 a^{3} + 6011 a^{2} - 30416 a - 2448\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-3\right){y}={x}^{3}+\left(2a^{5}+a^{4}-14a^{3}-5a^{2}+21a+1\right){x}^{2}+\left(102a^{5}-76a^{4}-608a^{3}+158a^{2}+848a+37\right){x}-2535a^{5}-1587a^{4}+18360a^{3}+6011a^{2}-30416a-2448$ |
| 41.1-c1 |
41.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1.104203791$ |
$602.8710960$ |
3.48622 |
\( \frac{28291562250468961}{41} a^{5} - \frac{75034507892957720}{41} a^{4} - \frac{74339093869733113}{41} a^{3} + \frac{322131433276155292}{41} a^{2} - \frac{194628191223625684}{41} a - \frac{17075969780280601}{41} \) |
\( \bigl[a^{2} - 2\) , \( a^{5} + a^{4} - 8 a^{3} - 6 a^{2} + 14 a + 6\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -22 a^{5} - a^{4} + 149 a^{3} + 6 a^{2} - 235 a - 11\) , \( 94 a^{5} + 14 a^{4} - 639 a^{3} - 95 a^{2} + 1025 a + 83\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-10a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-6a^{2}+14a+6\right){x}^{2}+\left(-22a^{5}-a^{4}+149a^{3}+6a^{2}-235a-11\right){x}+94a^{5}+14a^{4}-639a^{3}-95a^{2}+1025a+83$ |
| 41.1-c2 |
41.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.552101895$ |
$9645.937536$ |
3.48622 |
\( \frac{11140191868}{1681} a^{5} - \frac{20714282019}{1681} a^{4} - \frac{43465799391}{1681} a^{3} + \frac{94183101182}{1681} a^{2} - \frac{28243403954}{1681} a - \frac{2770439345}{1681} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{5} - a^{4} + 7 a^{3} + 6 a^{2} - 10 a - 6\) , \( a^{5} - 6 a^{3} + 8 a\) , \( a^{5} + 4 a^{4} + 2 a^{3} - 13 a^{2} - 12 a + 6\) , \( 16 a^{5} + 8 a^{4} - 96 a^{3} - 28 a^{2} + 140 a + 9\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{5}-6a^{3}+8a\right){y}={x}^{3}+\left(-a^{5}-a^{4}+7a^{3}+6a^{2}-10a-6\right){x}^{2}+\left(a^{5}+4a^{4}+2a^{3}-13a^{2}-12a+6\right){x}+16a^{5}+8a^{4}-96a^{3}-28a^{2}+140a+9$ |
| 41.1-c3 |
41.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{8} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.138025473$ |
$2411.484384$ |
3.48622 |
\( -\frac{119228256700129979876}{7984925229121} a^{5} + \frac{111287310461305511672}{7984925229121} a^{4} + \frac{822433090159920551049}{7984925229121} a^{3} - \frac{782233248396727566117}{7984925229121} a^{2} - \frac{1350050892675738930940}{7984925229121} a + \frac{1353169851196086606076}{7984925229121} \) |
\( \bigl[a^{5} - 6 a^{3} + 8 a\) , \( 2 a^{5} + a^{4} - 14 a^{3} - 6 a^{2} + 21 a + 4\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 19 a + 4\) , \( -a^{5} + 5 a^{4} + a^{3} - 16 a^{2} + 8 a + 3\) , \( 77 a^{5} + 23 a^{4} - 460 a^{3} - 134 a^{2} + 592 a + 45\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+8a\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+19a+4\right){y}={x}^{3}+\left(2a^{5}+a^{4}-14a^{3}-6a^{2}+21a+4\right){x}^{2}+\left(-a^{5}+5a^{4}+a^{3}-16a^{2}+8a+3\right){x}+77a^{5}+23a^{4}-460a^{3}-134a^{2}+592a+45$ |
| 41.1-c4 |
41.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.104203791$ |
$2411.484384$ |
3.48622 |
\( \frac{791094277061}{41} a^{5} + \frac{855665382862}{41} a^{4} - \frac{3756487777579}{41} a^{3} - \frac{2281929486711}{41} a^{2} + \frac{4743016300883}{41} a + \frac{380037390936}{41} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 9 a + 1\) , \( -a^{4} + a^{3} + 6 a^{2} - 4 a - 7\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 9 a + 4\) , \( 6 a^{3} - 3 a^{2} - 16 a + 13\) , \( 5 a^{5} - a^{4} - 25 a^{3} + 6 a^{2} + 33 a - 11\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+9a+1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+9a+4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-4a-7\right){x}^{2}+\left(6a^{3}-3a^{2}-16a+13\right){x}+5a^{5}-a^{4}-25a^{3}+6a^{2}+33a-11$ |
| 41.1-c5 |
41.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.276050947$ |
$9645.937536$ |
3.48622 |
\( \frac{23677855451970752823}{2825761} a^{5} + \frac{5053886051524373728}{2825761} a^{4} - \frac{159612382622855848143}{2825761} a^{3} - \frac{27935631605563081516}{2825761} a^{2} + \frac{250235952832496007036}{2825761} a + \frac{19512943195011698169}{2825761} \) |
\( \bigl[-a^{5} + 7 a^{3} - 11 a + 1\) , \( a^{5} + a^{4} - 8 a^{3} - 5 a^{2} + 14 a + 2\) , \( a^{2} + a - 2\) , \( -10 a^{5} - 17 a^{4} + 41 a^{3} + 55 a^{2} - 45 a - 32\) , \( 7 a^{5} - 6 a^{4} - 47 a^{3} + 43 a^{2} + 76 a - 76\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-11a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-5a^{2}+14a+2\right){x}^{2}+\left(-10a^{5}-17a^{4}+41a^{3}+55a^{2}-45a-32\right){x}+7a^{5}-6a^{4}-47a^{3}+43a^{2}+76a-76$ |
| 41.1-c6 |
41.1-c |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.552101895$ |
$602.8710960$ |
3.48622 |
\( \frac{349391736564802749544689038260}{1681} a^{5} + \frac{74575420690261073095227093976}{1681} a^{4} - \frac{2355249091000189081486082959641}{1681} a^{3} - \frac{412219716747166567264607798491}{1681} a^{2} + \frac{3692495472754704313872876101596}{1681} a + \frac{287934061614888155497139033860}{1681} \) |
\( \bigl[-a^{5} + 7 a^{3} - 11 a + 1\) , \( a^{5} + a^{4} - 8 a^{3} - 5 a^{2} + 14 a + 2\) , \( a^{2} + a - 2\) , \( 50 a^{5} + 58 a^{4} - 229 a^{3} - 165 a^{2} + 275 a + 53\) , \( -166 a^{5} - 221 a^{4} + 742 a^{3} + 674 a^{2} - 881 a - 329\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-11a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-5a^{2}+14a+2\right){x}^{2}+\left(50a^{5}+58a^{4}-229a^{3}-165a^{2}+275a+53\right){x}-166a^{5}-221a^{4}+742a^{3}+674a^{2}-881a-329$ |
| 41.1-d1 |
41.1-d |
$1$ |
$1$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2562.859668$ |
2.23694 |
\( \frac{17581014}{41} a^{5} + \frac{909122}{41} a^{4} - \frac{101266615}{41} a^{3} - \frac{8315018}{41} a^{2} + \frac{112636597}{41} a + \frac{8277012}{41} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a + 1\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 19 a + 4\) , \( a^{5} - 6 a^{3} + a^{2} + 8 a - 2\) , \( -3 a^{5} + 13 a^{4} - 54 a^{2} + 48 a + 6\) , \( -16 a^{5} + 44 a^{4} + 38 a^{3} - 186 a^{2} + 120 a + 9\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+11a+1\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+8a-2\right){y}={x}^{3}+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+19a+4\right){x}^{2}+\left(-3a^{5}+13a^{4}-54a^{2}+48a+6\right){x}-16a^{5}+44a^{4}+38a^{3}-186a^{2}+120a+9$ |
| 41.1-e1 |
41.1-e |
$2$ |
$2$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{10} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$871.1270664$ |
1.52069 |
\( -\frac{17346915788074079314836584}{13422659310152401} a^{5} - \frac{8581709707447170973412624}{13422659310152401} a^{4} + \frac{108601346392361890101409788}{13422659310152401} a^{3} + \frac{40899069062364745211096796}{13422659310152401} a^{2} - \frac{147031171059965501423455549}{13422659310152401} a - \frac{11605478104821993385452654}{13422659310152401} \) |
\( \bigl[a^{3} - 2 a + 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a - 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -6 a^{5} + 5 a^{4} + 32 a^{3} - 19 a^{2} - 28 a - 4\) , \( a^{5} + 10 a^{4} - 18 a^{3} - 44 a^{2} + 62 a + 8\bigr] \) |
${y}^2+\left(a^{3}-2a+2\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-10a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-4a^{2}+14a-1\right){x}^{2}+\left(-6a^{5}+5a^{4}+32a^{3}-19a^{2}-28a-4\right){x}+a^{5}+10a^{4}-18a^{3}-44a^{2}+62a+8$ |
| 41.1-e2 |
41.1-e |
$2$ |
$2$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{5} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1742.254132$ |
1.52069 |
\( \frac{3780334519552}{115856201} a^{5} + \frac{2006359760792}{115856201} a^{4} - \frac{23167912790280}{115856201} a^{3} - \frac{8351011049247}{115856201} a^{2} + \frac{32253176592092}{115856201} a + \frac{2582626205540}{115856201} \) |
\( \bigl[a^{3} - 2 a + 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a - 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 13 a + 1\) , \( -3 a^{5} + 2 a^{4} + 18 a^{3} - 6 a^{2} - 22 a - 2\bigr] \) |
${y}^2+\left(a^{3}-2a+2\right){x}{y}+\left(-a^{5}+7a^{3}+a^{2}-10a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-8a^{3}-4a^{2}+14a-1\right){x}^{2}+\left(-a^{5}+7a^{3}+a^{2}-13a+1\right){x}-3a^{5}+2a^{4}+18a^{3}-6a^{2}-22a-2$ |
| 41.1-f1 |
41.1-f |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12006.50007$ |
2.61991 |
\( \frac{650430828652}{41} a^{5} - \frac{1741104974931}{41} a^{4} - \frac{1633571237965}{41} a^{3} + \frac{7292594106543}{41} a^{2} - \frac{4423451462754}{41} a - \frac{387897316333}{41} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 7 a + 1\) , \( a^{5} - 6 a^{3} + 8 a + 1\) , \( 4 a^{5} - a^{4} - 19 a^{3} + 6 a^{2} + 19 a - 4\) , \( -18 a^{5} - 20 a^{4} + 89 a^{3} + 51 a^{2} - 115 a - 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{5}-6a^{3}+8a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-7a+1\right){x}^{2}+\left(4a^{5}-a^{4}-19a^{3}+6a^{2}+19a-4\right){x}-18a^{5}-20a^{4}+89a^{3}+51a^{2}-115a-5$ |
| 41.1-f2 |
41.1-f |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12006.50007$ |
2.61991 |
\( \frac{25627932}{41} a^{5} + \frac{4908779}{41} a^{4} - \frac{173810481}{41} a^{3} - \frac{27920962}{41} a^{2} + \frac{275379869}{41} a + \frac{21678892}{41} \) |
\( \bigl[-a^{5} + 7 a^{3} - 10 a + 1\) , \( -a^{4} + 4 a^{2} - a\) , \( a\) , \( -a^{5} - 3 a^{4} + 6 a^{3} + 11 a^{2} - 12 a - 2\) , \( -9 a^{5} - 10 a^{4} + 46 a^{3} + 29 a^{2} - 64 a - 5\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-10a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+4a^{2}-a\right){x}^{2}+\left(-a^{5}-3a^{4}+6a^{3}+11a^{2}-12a-2\right){x}-9a^{5}-10a^{4}+46a^{3}+29a^{2}-64a-5$ |
| 41.1-f3 |
41.1-f |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$24013.00015$ |
2.61991 |
\( -\frac{2533710179}{1681} a^{5} + \frac{2709215657}{1681} a^{4} + \frac{17781702603}{1681} a^{3} - \frac{19180097313}{1681} a^{2} - \frac{29907800321}{1681} a + \frac{33557868958}{1681} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 6 a^{3} - 7 a + 1\) , \( a^{4} - 4 a^{2} + 2\) , \( 3 a^{5} + 3 a^{4} - 18 a^{3} - 14 a^{2} + 23 a + 2\) , \( 4 a^{5} + 3 a^{4} - 24 a^{3} - 14 a^{2} + 30 a + 2\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-7a+1\right){x}^{2}+\left(3a^{5}+3a^{4}-18a^{3}-14a^{2}+23a+2\right){x}+4a^{5}+3a^{4}-24a^{3}-14a^{2}+30a+2$ |
| 41.1-f4 |
41.1-f |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{4} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1500.812509$ |
2.61991 |
\( -\frac{93141780100309994200}{2825761} a^{5} + \frac{100392272347858888757}{2825761} a^{4} + \frac{644225672853580557397}{2825761} a^{3} - \frac{702093009464056054451}{2825761} a^{2} - \frac{1063280100014133478356}{2825761} a + \frac{1200350168830066620739}{2825761} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 6 a^{3} - 7 a + 1\) , \( a^{4} - 4 a^{2} + 2\) , \( -22 a^{5} - 12 a^{4} + 132 a^{3} + 56 a^{2} - 162 a - 13\) , \( -66 a^{5} - 32 a^{4} + 417 a^{3} + 152 a^{2} - 576 a - 46\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-7a+1\right){x}^{2}+\left(-22a^{5}-12a^{4}+132a^{3}+56a^{2}-162a-13\right){x}-66a^{5}-32a^{4}+417a^{3}+152a^{2}-576a-46$ |
| 41.1-g1 |
41.1-g |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.368452691$ |
$5158.289353$ |
2.48833 |
\( \frac{650430828652}{41} a^{5} - \frac{1741104974931}{41} a^{4} - \frac{1633571237965}{41} a^{3} + \frac{7292594106543}{41} a^{2} - \frac{4423451462754}{41} a - \frac{387897316333}{41} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 9 a + 5\) , \( a^{4} - 4 a^{2} - a\) , \( 1\) , \( 8 a^{5} + 8 a^{4} - 54 a^{3} - 33 a^{2} + 87 a + 3\) , \( 11 a^{5} - 6 a^{4} - 57 a^{3} + 30 a^{2} + 49 a - 19\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+9a+5\right){x}{y}+{y}={x}^{3}+\left(a^{4}-4a^{2}-a\right){x}^{2}+\left(8a^{5}+8a^{4}-54a^{3}-33a^{2}+87a+3\right){x}+11a^{5}-6a^{4}-57a^{3}+30a^{2}+49a-19$ |
| 41.1-g2 |
41.1-g |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.092113172$ |
$82532.62965$ |
2.48833 |
\( \frac{25627932}{41} a^{5} + \frac{4908779}{41} a^{4} - \frac{173810481}{41} a^{3} - \frac{27920962}{41} a^{2} + \frac{275379869}{41} a + \frac{21678892}{41} \) |
\( \bigl[1\) , \( 2 a^{5} - 13 a^{3} + a^{2} + 18 a - 5\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a + 1\) , \( 2 a^{4} - 11 a^{2} - a + 11\) , \( -10 a^{5} - 7 a^{4} + 64 a^{3} + 33 a^{2} - 92 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a+1\right){y}={x}^{3}+\left(2a^{5}-13a^{3}+a^{2}+18a-5\right){x}^{2}+\left(2a^{4}-11a^{2}-a+11\right){x}-10a^{5}-7a^{4}+64a^{3}+33a^{2}-92a-13$ |
| 41.1-g3 |
41.1-g |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.184226345$ |
$20633.15741$ |
2.48833 |
\( -\frac{2533710179}{1681} a^{5} + \frac{2709215657}{1681} a^{4} + \frac{17781702603}{1681} a^{3} - \frac{19180097313}{1681} a^{2} - \frac{29907800321}{1681} a + \frac{33557868958}{1681} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 3\) , \( a^{2} + a - 2\) , \( 2 a^{5} - 13 a^{3} + a^{2} + 20 a - 4\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(a^{2}+a-2\right){x}+2a^{5}-13a^{3}+a^{2}+20a-4$ |
| 41.1-g4 |
41.1-g |
$4$ |
$4$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{4} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.368452691$ |
$322.3930845$ |
2.48833 |
\( -\frac{93141780100309994200}{2825761} a^{5} + \frac{100392272347858888757}{2825761} a^{4} + \frac{644225672853580557397}{2825761} a^{3} - \frac{702093009464056054451}{2825761} a^{2} - \frac{1063280100014133478356}{2825761} a + \frac{1200350168830066620739}{2825761} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 3\) , \( 10 a^{5} - 5 a^{4} - 70 a^{3} + 36 a^{2} + 116 a - 67\) , \( 14 a^{5} - 20 a^{4} - 101 a^{3} + 134 a^{2} + 172 a - 225\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(10a^{5}-5a^{4}-70a^{3}+36a^{2}+116a-67\right){x}+14a^{5}-20a^{4}-101a^{3}+134a^{2}+172a-225$ |
| 41.1-h1 |
41.1-h |
$2$ |
$2$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{10} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.077237942$ |
$2766.209276$ |
2.79729 |
\( -\frac{17346915788074079314836584}{13422659310152401} a^{5} - \frac{8581709707447170973412624}{13422659310152401} a^{4} + \frac{108601346392361890101409788}{13422659310152401} a^{3} + \frac{40899069062364745211096796}{13422659310152401} a^{2} - \frac{147031171059965501423455549}{13422659310152401} a - \frac{11605478104821993385452654}{13422659310152401} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 4 a^{2}\) , \( -a^{5} + 7 a^{3} - 10 a + 2\) , \( 7 a^{5} - 27 a^{4} + 4 a^{3} + 72 a^{2} - 57 a - 2\) , \( 62 a^{5} - 193 a^{4} - 57 a^{3} + 569 a^{2} - 368 a - 34\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-a^{5}+7a^{3}-10a+2\right){y}={x}^{3}+\left(a^{4}-4a^{2}\right){x}^{2}+\left(7a^{5}-27a^{4}+4a^{3}+72a^{2}-57a-2\right){x}+62a^{5}-193a^{4}-57a^{3}+569a^{2}-368a-34$ |
| 41.1-h2 |
41.1-h |
$2$ |
$2$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{5} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.038618971$ |
$11064.83710$ |
2.79729 |
\( \frac{3780334519552}{115856201} a^{5} + \frac{2006359760792}{115856201} a^{4} - \frac{23167912790280}{115856201} a^{3} - \frac{8351011049247}{115856201} a^{2} + \frac{32253176592092}{115856201} a + \frac{2582626205540}{115856201} \) |
\( \bigl[1\) , \( 2 a^{5} - 13 a^{3} + a^{2} + 20 a - 5\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 11 a + 3\) , \( -2 a^{5} + a^{4} + 15 a^{3} - 6 a^{2} - 28 a + 10\) , \( -4 a^{4} + 2 a^{3} + 19 a^{2} - 7 a - 11\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+11a+3\right){y}={x}^{3}+\left(2a^{5}-13a^{3}+a^{2}+20a-5\right){x}^{2}+\left(-2a^{5}+a^{4}+15a^{3}-6a^{2}-28a+10\right){x}-4a^{4}+2a^{3}+19a^{2}-7a-11$ |
| 41.1-i1 |
41.1-i |
$1$ |
$1$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.004504421$ |
$130244.6422$ |
3.07241 |
\( \frac{17581014}{41} a^{5} + \frac{909122}{41} a^{4} - \frac{101266615}{41} a^{3} - \frac{8315018}{41} a^{2} + \frac{112636597}{41} a + \frac{8277012}{41} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 19 a + 3\) , \( a^{4} - 5 a^{2} - a + 4\) , \( a^{5} - 6 a^{3} + a^{2} + 8 a - 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 2 a + 10\) , \( 46 a^{5} + 9 a^{4} - 309 a^{3} - 52 a^{2} + 483 a + 38\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+19a+3\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+8a-3\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+4\right){x}^{2}+\left(2a^{4}-a^{3}-10a^{2}+2a+10\right){x}+46a^{5}+9a^{4}-309a^{3}-52a^{2}+483a+38$ |
| 41.1-j1 |
41.1-j |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$247.6333259$ |
0.864567 |
\( \frac{28291562250468961}{41} a^{5} - \frac{75034507892957720}{41} a^{4} - \frac{74339093869733113}{41} a^{3} + \frac{322131433276155292}{41} a^{2} - \frac{194628191223625684}{41} a - \frac{17075969780280601}{41} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 8 a - 3\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a + 1\) , \( -72 a^{5} + 196 a^{4} + 166 a^{3} - 810 a^{2} + 558 a - 17\) , \( 1093 a^{5} - 2903 a^{4} - 2799 a^{3} + 12183 a^{2} - 7185 a - 802\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+11a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+5a^{2}-8a-3\right){x}^{2}+\left(-72a^{5}+196a^{4}+166a^{3}-810a^{2}+558a-17\right){x}+1093a^{5}-2903a^{4}-2799a^{3}+12183a^{2}-7185a-802$ |
| 41.1-j2 |
41.1-j |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$7924.266431$ |
0.864567 |
\( \frac{11140191868}{1681} a^{5} - \frac{20714282019}{1681} a^{4} - \frac{43465799391}{1681} a^{3} + \frac{94183101182}{1681} a^{2} - \frac{28243403954}{1681} a - \frac{2770439345}{1681} \) |
\( \bigl[a^{5} - 6 a^{3} + 9 a\) , \( -2 a^{5} + 13 a^{3} - 18 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 13 a^{2} + 35 a - 26\) , \( 8 a^{5} - 12 a^{4} - 44 a^{3} + 65 a^{2} + 49 a - 73\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+9a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-2a^{5}+13a^{3}-18a+1\right){x}^{2}+\left(3a^{5}-2a^{4}-20a^{3}+13a^{2}+35a-26\right){x}+8a^{5}-12a^{4}-44a^{3}+65a^{2}+49a-73$ |
| 41.1-j3 |
41.1-j |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{8} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1981.066607$ |
0.864567 |
\( -\frac{119228256700129979876}{7984925229121} a^{5} + \frac{111287310461305511672}{7984925229121} a^{4} + \frac{822433090159920551049}{7984925229121} a^{3} - \frac{782233248396727566117}{7984925229121} a^{2} - \frac{1350050892675738930940}{7984925229121} a + \frac{1353169851196086606076}{7984925229121} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 4\) , \( -2 a^{5} - a^{4} + 14 a^{3} + 4 a^{2} - 21 a + 1\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a + 1\) , \( 4 a^{5} - 7 a^{4} - 33 a^{3} + 57 a^{2} + 65 a - 100\) , \( -18 a^{5} + 14 a^{4} + 135 a^{3} - 121 a^{2} - 231 a + 234\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+4\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+11a+1\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+14a^{3}+4a^{2}-21a+1\right){x}^{2}+\left(4a^{5}-7a^{4}-33a^{3}+57a^{2}+65a-100\right){x}-18a^{5}+14a^{4}+135a^{3}-121a^{2}-231a+234$ |
| 41.1-j4 |
41.1-j |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3962.133215$ |
0.864567 |
\( \frac{791094277061}{41} a^{5} + \frac{855665382862}{41} a^{4} - \frac{3756487777579}{41} a^{3} - \frac{2281929486711}{41} a^{2} + \frac{4743016300883}{41} a + \frac{380037390936}{41} \) |
\( \bigl[a^{2} - 3\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 6 a^{2} + 31 a + 5\) , \( a + 1\) , \( 7 a^{5} + 2 a^{4} - 47 a^{3} - 14 a^{2} + 74 a + 17\) , \( 6 a^{5} + a^{4} - 39 a^{3} - 8 a^{2} + 58 a + 10\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}-6a^{2}+31a+5\right){x}^{2}+\left(7a^{5}+2a^{4}-47a^{3}-14a^{2}+74a+17\right){x}+6a^{5}+a^{4}-39a^{3}-8a^{2}+58a+10$ |
| 41.1-j5 |
41.1-j |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$7924.266431$ |
0.864567 |
\( \frac{23677855451970752823}{2825761} a^{5} + \frac{5053886051524373728}{2825761} a^{4} - \frac{159612382622855848143}{2825761} a^{3} - \frac{27935631605563081516}{2825761} a^{2} + \frac{250235952832496007036}{2825761} a + \frac{19512943195011698169}{2825761} \) |
\( \bigl[a\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 2\) , \( 12 a^{5} + 6 a^{4} - 83 a^{3} - 19 a^{2} + 132 a - 30\) , \( -39 a^{5} - 7 a^{4} + 253 a^{3} + 8 a^{2} - 372 a + 104\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}+a^{2}+7a-2\right){x}^{2}+\left(12a^{5}+6a^{4}-83a^{3}-19a^{2}+132a-30\right){x}-39a^{5}-7a^{4}+253a^{3}+8a^{2}-372a+104$ |
| 41.1-j6 |
41.1-j |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$495.2666519$ |
0.864567 |
\( \frac{349391736564802749544689038260}{1681} a^{5} + \frac{74575420690261073095227093976}{1681} a^{4} - \frac{2355249091000189081486082959641}{1681} a^{3} - \frac{412219716747166567264607798491}{1681} a^{2} + \frac{3692495472754704313872876101596}{1681} a + \frac{287934061614888155497139033860}{1681} \) |
\( \bigl[a\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 2\) , \( 177 a^{5} + 86 a^{4} - 1098 a^{3} - 419 a^{2} + 1457 a + 155\) , \( -1660 a^{5} - 836 a^{4} + 10483 a^{3} + 3885 a^{2} - 14448 a - 742\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}+a^{2}+9a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}+a^{2}+7a-2\right){x}^{2}+\left(177a^{5}+86a^{4}-1098a^{3}-419a^{2}+1457a+155\right){x}-1660a^{5}-836a^{4}+10483a^{3}+3885a^{2}-14448a-742$ |
| 41.1-k1 |
41.1-k |
$2$ |
$7$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \) |
$0.144014981$ |
$2871.172395$ |
4.33089 |
\( -\frac{1669545727}{1681} a^{5} - \frac{356208233}{1681} a^{4} + \frac{11254384379}{1681} a^{3} + \frac{1969603507}{1681} a^{2} - \frac{17644006659}{1681} a - \frac{1376569651}{1681} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( -7 a^{5} - 2 a^{4} + 46 a^{3} + 14 a^{2} - 62 a - 3\) , \( -62 a^{5} - 29 a^{4} + 393 a^{3} + 145 a^{2} - 534 a - 43\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-7a^{5}-2a^{4}+46a^{3}+14a^{2}-62a-3\right){x}-62a^{5}-29a^{4}+393a^{3}+145a^{2}-534a-43$ |
| 41.1-k2 |
41.1-k |
$2$ |
$7$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{14} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \cdot 7 \) |
$1.008104867$ |
$58.59535501$ |
4.33089 |
\( \frac{3994507357674741603296625125869374470}{37929227194915558802161} a^{5} + \frac{1976118326644757612365959956611161273}{37929227194915558802161} a^{4} - \frac{25007829804251700012032562188202123255}{37929227194915558802161} a^{3} - \frac{9417874613411500255981970467083831998}{37929227194915558802161} a^{2} + \frac{33857106961303163824780707970707024449}{37929227194915558802161} a + \frac{2672431597592452105549243894349194373}{37929227194915558802161} \) |
\( \bigl[a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 12 a\) , \( -a^{4} + 4 a^{2} - a\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( -180 a^{5} + 615 a^{4} + 276 a^{3} - 2589 a^{2} + 1958 a + 138\) , \( 5561 a^{5} - 14481 a^{4} - 14589 a^{3} + 60556 a^{2} - 35176 a - 3037\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+12a\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-5a^{2}+12a+4\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a\right){x}^{2}+\left(-180a^{5}+615a^{4}+276a^{3}-2589a^{2}+1958a+138\right){x}+5561a^{5}-14481a^{4}-14589a^{3}+60556a^{2}-35176a-3037$ |
| 41.1-l1 |
41.1-l |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.098279859$ |
$5215.505626$ |
2.68437 |
\( -\frac{8984179006241268697160}{41} a^{5} - \frac{4444553688617899720556}{41} a^{4} + \frac{56245938903177637867836}{41} a^{3} + \frac{21182054771657449538079}{41} a^{2} - \frac{76149141402730689873442}{41} a - \frac{6010654485773269437037}{41} \) |
\( \bigl[a + 1\) , \( -a^{5} - a^{4} + 8 a^{3} + 5 a^{2} - 13 a - 1\) , \( a^{4} - 5 a^{2} + 4\) , \( 82 a^{5} - 22 a^{4} - 553 a^{3} + 227 a^{2} + 876 a - 575\) , \( -546 a^{5} + 476 a^{4} + 3673 a^{3} - 3323 a^{2} - 5775 a + 5742\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(-a^{5}-a^{4}+8a^{3}+5a^{2}-13a-1\right){x}^{2}+\left(82a^{5}-22a^{4}-553a^{3}+227a^{2}+876a-575\right){x}-546a^{5}+476a^{4}+3673a^{3}-3323a^{2}-5775a+5742$ |
| 41.1-l2 |
41.1-l |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.049139929$ |
$83448.09002$ |
2.68437 |
\( -\frac{14597338066672}{1681} a^{5} - \frac{7221408650287}{1681} a^{4} + \frac{91387418873252}{1681} a^{3} + \frac{34416098786654}{1681} a^{2} - \frac{123725798041612}{1681} a - \frac{9765838570959}{1681} \) |
\( \bigl[a + 1\) , \( -a^{5} - a^{4} + 8 a^{3} + 5 a^{2} - 13 a - 1\) , \( a^{4} - 5 a^{2} + 4\) , \( 2 a^{5} - 2 a^{4} - 13 a^{3} + 22 a^{2} + 26 a - 40\) , \( -5 a^{5} + 10 a^{4} + 38 a^{3} - 58 a^{2} - 63 a + 85\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(-a^{5}-a^{4}+8a^{3}+5a^{2}-13a-1\right){x}^{2}+\left(2a^{5}-2a^{4}-13a^{3}+22a^{2}+26a-40\right){x}-5a^{5}+10a^{4}+38a^{3}-58a^{2}-63a+85$ |
| 41.1-l3 |
41.1-l |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.098279859$ |
$20862.02250$ |
2.68437 |
\( \frac{1260951708}{41} a^{5} + \frac{269913471}{41} a^{4} - \frac{8498646764}{41} a^{3} - \frac{1490592607}{41} a^{2} + \frac{13320684705}{41} a + \frac{1038742621}{41} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{5} - a^{4} + 8 a^{3} + 4 a^{2} - 13 a + 2\) , \( a^{5} - 6 a^{3} + 8 a + 1\) , \( 2 a^{5} - 4 a^{4} - 3 a^{3} + 20 a^{2} - 17 a + 2\) , \( -a^{5} + 7 a^{4} + 3 a^{3} - 26 a^{2} + 13 a + 3\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{5}-6a^{3}+8a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+8a^{3}+4a^{2}-13a+2\right){x}^{2}+\left(2a^{5}-4a^{4}-3a^{3}+20a^{2}-17a+2\right){x}-a^{5}+7a^{4}+3a^{3}-26a^{2}+13a+3$ |
| 41.1-l4 |
41.1-l |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.024569964$ |
$83448.09002$ |
2.68437 |
\( -\frac{168461786556360}{2825761} a^{5} + \frac{511716866081588}{2825761} a^{4} + \frac{138562484540900}{2825761} a^{3} - \frac{1462387435858103}{2825761} a^{2} + \frac{953194658002650}{2825761} a + \frac{82830457729933}{2825761} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 20 a + 3\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 20 a - 2\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a + 1\) , \( -4 a^{5} - 7 a^{4} + 33 a^{3} + 28 a^{2} - 59 a - 17\) , \( -2 a^{5} + 5 a^{4} + a^{3} - 12 a^{2} + 13 a - 5\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+20a+3\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a+1\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+5a^{2}-20a-2\right){x}^{2}+\left(-4a^{5}-7a^{4}+33a^{3}+28a^{2}-59a-17\right){x}-2a^{5}+5a^{4}+a^{3}-12a^{2}+13a-5$ |
| 41.1-l5 |
41.1-l |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{8} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.049139929$ |
$5215.505626$ |
2.68437 |
\( \frac{885542140797128688333102}{7984925229121} a^{5} + \frac{955794109593857013122388}{7984925229121} a^{4} - \frac{4203761130028915963020406}{7984925229121} a^{3} - \frac{2546762038792787355090604}{7984925229121} a^{2} + \frac{5302368119779655229510389}{7984925229121} a + \frac{424835420971664723996149}{7984925229121} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - 5 a^{2} + 20 a + 3\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 20 a - 2\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a + 1\) , \( 11 a^{5} - 17 a^{4} - 77 a^{3} + 98 a^{2} + 131 a - 152\) , \( 72 a^{5} - 51 a^{4} - 499 a^{3} + 400 a^{2} + 821 a - 736\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-5a^{2}+20a+3\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-4a^{2}+20a+1\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+5a^{2}-20a-2\right){x}^{2}+\left(11a^{5}-17a^{4}-77a^{3}+98a^{2}+131a-152\right){x}+72a^{5}-51a^{4}-499a^{3}+400a^{2}+821a-736$ |
| 41.1-l6 |
41.1-l |
$6$ |
$8$ |
6.6.1312625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$139.51071$ |
$(a^5-7a^3-a^2+12a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.049139929$ |
$20862.02250$ |
2.68437 |
\( -\frac{197905866363742218686}{1681} a^{5} + \frac{600671715893159422284}{1681} a^{4} + \frac{162890925250602345366}{1681} a^{3} - \frac{1716846659406171103780}{1681} a^{2} + \frac{1119150351391201832075}{1681} a + \frac{97244421297428052459}{1681} \) |
\( \bigl[a^{5} - 6 a^{3} + 8 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a\) , \( -2 a^{5} - 2 a^{4} + 18 a^{3} + 4 a^{2} - 37 a + 13\) , \( 3 a^{5} - 21 a^{3} + 7 a^{2} + 31 a - 17\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+8a+1\right){x}{y}+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+11a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-2a^{5}-2a^{4}+18a^{3}+4a^{2}-37a+13\right){x}+3a^{5}-21a^{3}+7a^{2}+31a-17$ |
*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.
