| 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 |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{7} \) |
$92.81049$ |
$(3a^5-2a^4-17a^3+10a^2+16a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1063.531897$ |
1.26800 |
\( -\frac{113153543237056}{62748517} a^{5} - \frac{42457887805007}{62748517} a^{4} + \frac{488800883589612}{62748517} a^{3} - \frac{44516784604511}{62748517} a^{2} - \frac{385469849640510}{62748517} a + \frac{44534588204426}{62748517} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 11 a^{2} + 17 a - 4\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 7 a - 2\) , \( 10 a^{5} - 4 a^{4} - 54 a^{3} + 24 a^{2} + 51 a - 5\) , \( 25 a^{5} - 12 a^{4} - 142 a^{3} + 65 a^{2} + 147 a - 17\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+11a^{2}+17a-4\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+7a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+1\right){x}^{2}+\left(10a^{5}-4a^{4}-54a^{3}+24a^{2}+51a-5\right){x}+25a^{5}-12a^{4}-142a^{3}+65a^{2}+147a-17$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{7} \) |
$92.81049$ |
$(3a^5-2a^4-17a^3+10a^2+16a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.002349118$ |
$17461.84080$ |
2.05407 |
\( \frac{33889457777}{62748517} a^{5} - \frac{83113788886}{62748517} a^{4} - \frac{102300181186}{62748517} a^{3} + \frac{371472408155}{62748517} a^{2} - \frac{227617587843}{62748517} a + \frac{15310089083}{62748517} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 3\) , \( -a^{5} + 7 a^{3} - a^{2} - 9 a + 2\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -a^{5} - a^{4} + 8 a^{3} + 5 a^{2} - 20 a + 6\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 16 a^{2} - a - 2\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-3\right){x}{y}+\left(a^{5}-6a^{3}+8a+2\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-a^{2}-9a+2\right){x}^{2}+\left(-a^{5}-a^{4}+8a^{3}+5a^{2}-20a+6\right){x}+2a^{5}-4a^{4}-8a^{3}+16a^{2}-a-2$ |
| 13.2-a1 |
13.2-a |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
13.2 |
\( 13 \) |
\( 13^{7} \) |
$92.81049$ |
$(-a^5+a^4+5a^3-5a^2-3a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1063.531897$ |
1.26800 |
\( \frac{255013799509031}{62748517} a^{5} - \frac{477311078347916}{62748517} a^{4} - \frac{1339962421221462}{62748517} a^{3} + \frac{2643361615369126}{62748517} a^{2} + \frac{858722677391412}{62748517} a - \frac{2230501197703405}{62748517} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 11 a - 2\) , \( -a - 1\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 10 a\) , \( 3 a^{5} + 4 a^{4} - 9 a^{3} - 7 a^{2} + 4 a\) , \( 23 a^{5} + 2 a^{4} - 113 a^{3} + 25 a^{2} + 99 a - 12\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+6a^{2}+11a-2\right){x}{y}+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+10a\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a^{5}+4a^{4}-9a^{3}-7a^{2}+4a\right){x}+23a^{5}+2a^{4}-113a^{3}+25a^{2}+99a-12$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{7} \) |
$92.81049$ |
$(-a^5+a^4+5a^3-5a^2-3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.002349118$ |
$17461.84080$ |
2.05407 |
\( -\frac{379829569709}{62748517} a^{5} + \frac{185472136849}{62748517} a^{4} + \frac{2177940852778}{62748517} a^{3} - \frac{883264147970}{62748517} a^{2} - \frac{2091604847718}{62748517} a + \frac{253378952210}{62748517} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 10 a - 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( a^{2} - 2\) , \( 4 a^{5} - 2 a^{4} - 22 a^{3} + 10 a^{2} + 19 a + 2\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 8 a^{2} - 23 a + 1\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+10a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){x}^{2}+\left(4a^{5}-2a^{4}-22a^{3}+10a^{2}+19a+2\right){x}-3a^{5}+2a^{4}+19a^{3}-8a^{2}-23a+1$ |
| 13.3-a1 |
13.3-a |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
13.3 |
\( 13 \) |
\( 13^{5} \) |
$92.81049$ |
$(-2a^5+a^4+12a^3-4a^2-13a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.001923217$ |
$31237.66280$ |
2.14881 |
\( \frac{341618999984}{371293} a^{5} - \frac{652186405930}{371293} a^{4} - \frac{1777962603488}{371293} a^{3} + \frac{3602250670634}{371293} a^{2} + \frac{1073690215744}{371293} a - \frac{3003492585005}{371293} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 10 a - 1\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a\) , \( a^{2} - 2\) , \( 2 a^{4} - a^{3} - 2 a^{2}\) , \( a^{5} + 3 a^{4} - 10 a^{3} + 9 a - 2\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+10a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}+a^{2}+7a\right){x}^{2}+\left(2a^{4}-a^{3}-2a^{2}\right){x}+a^{5}+3a^{4}-10a^{3}+9a-2$ |
| 13.4-a1 |
13.4-a |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
13.4 |
\( 13 \) |
\( 13^{5} \) |
$92.81049$ |
$(-2a^5+a^4+12a^3-5a^2-14a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.001923217$ |
$31237.66280$ |
2.14881 |
\( -\frac{212547114746}{371293} a^{5} - \frac{28453046632}{371293} a^{4} + \frac{1003531292060}{371293} a^{3} - \frac{199053407824}{371293} a^{2} - \frac{850826471640}{371293} a + \frac{100365149545}{371293} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 14 a - 3\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 5 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( a^{5} - 4 a^{3} + a^{2} - a + 5\) , \( a^{5} - 5 a^{3} + 5 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+6a^{2}+14a-3\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-4\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-5a+4\right){x}^{2}+\left(a^{5}-4a^{3}+a^{2}-a+5\right){x}+a^{5}-5a^{3}+5a+2$ |
| 41.3-a1 |
41.3-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41^{10} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$813.8692778$ |
1.94068 |
\( \frac{3683207165193102481237192}{13422659310152401} a^{5} - \frac{1642339292420493726158390}{13422659310152401} a^{4} - \frac{20474623287319134176284544}{13422659310152401} a^{3} + \frac{229842362061702235031886}{327381934393961} a^{2} + \frac{20619800140158338304997594}{13422659310152401} a - \frac{2484108563337772728271739}{13422659310152401} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 1\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -49 a^{5} + 35 a^{4} + 281 a^{3} - 160 a^{2} - 275 a + 11\) , \( 136 a^{5} - 103 a^{4} - 781 a^{3} + 472 a^{2} + 745 a - 62\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-2\right){x}{y}+\left(a^{5}-6a^{3}+8a+2\right){y}={x}^{3}+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+13a-1\right){x}^{2}+\left(-49a^{5}+35a^{4}+281a^{3}-160a^{2}-275a+11\right){x}+136a^{5}-103a^{4}-781a^{3}+472a^{2}+745a-62$ |
| 41.3-a2 |
41.3-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41^{5} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6510.954223$ |
1.94068 |
\( \frac{7619330091674956}{115856201} a^{5} - \frac{22560326971775052}{115856201} a^{4} - \frac{16506025526903560}{115856201} a^{3} + \frac{2434179943733724}{2825761} a^{2} - \frac{80280553523802984}{115856201} a + \frac{7994447419048309}{115856201} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 1\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( a^{5} + 5 a^{4} - 14 a^{3} - 20 a^{2} + 40 a - 9\) , \( 12 a^{5} - 24 a^{4} - 45 a^{3} + 110 a^{2} - 43 a - 8\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-2\right){x}{y}+\left(a^{5}-6a^{3}+8a+2\right){y}={x}^{3}+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+13a-1\right){x}^{2}+\left(a^{5}+5a^{4}-14a^{3}-20a^{2}+40a-9\right){x}+12a^{5}-24a^{4}-45a^{3}+110a^{2}-43a-8$ |
| 41.3-b1 |
41.3-b |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41 \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$4678.254988$ |
1.39442 |
\( -\frac{716692}{41} a^{5} - \frac{23636420}{41} a^{4} + \frac{7907999}{41} a^{3} + 3338087 a^{2} - \frac{149688851}{41} a + \frac{15615439}{41} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 10 a - 3\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{5} + a^{4} - 10 a^{3} - 3 a^{2} + 10 a + 5\) , \( 0\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+6a^{2}+10a-3\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-6a+5\right){x}^{2}+\left(2a^{5}+a^{4}-10a^{3}-3a^{2}+10a+5\right){x}$ |
| 41.3-b2 |
41.3-b |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( - 41^{2} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$584.7818735$ |
1.39442 |
\( \frac{4227054751862476}{1681} a^{5} - \frac{8907862174714698}{1681} a^{4} - \frac{12146939919480105}{1681} a^{3} + \frac{1004240536533933}{41} a^{2} - \frac{27544926363068101}{1681} a + \frac{2659697336777508}{1681} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 10 a\) , \( a^{4} - 6 a^{2} + a + 6\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 14 a - 2\) , \( -19 a^{5} + 17 a^{4} + 104 a^{3} - 82 a^{2} - 82 a + 23\) , \( -22 a^{5} + 24 a^{4} + 107 a^{3} - 112 a^{2} - 37 a + 12\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+10a\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+6a^{2}+14a-2\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+6\right){x}^{2}+\left(-19a^{5}+17a^{4}+104a^{3}-82a^{2}-82a+23\right){x}-22a^{5}+24a^{4}+107a^{3}-112a^{2}-37a+12$ |
| 41.3-c1 |
41.3-c |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41 \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1351.437236$ |
1.61126 |
\( -\frac{8584162099}{41} a^{5} + \frac{25376641760}{41} a^{4} + \frac{18654917222}{41} a^{3} - 2738133595 a^{2} + \frac{90181405656}{41} a - \frac{8977485322}{41} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 7 a - 1\) , \( -a^{4} + 4 a^{2} - 2 a - 2\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 10 a - 6\) , \( -a^{5} - a^{4} + 6 a^{3} + 4 a^{2} - 9 a - 2\) , \( 4 a^{5} - 18 a^{3} + 8 a^{2} + 13 a - 8\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+7a-1\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+11a^{2}+10a-6\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-2a-2\right){x}^{2}+\left(-a^{5}-a^{4}+6a^{3}+4a^{2}-9a-2\right){x}+4a^{5}-18a^{3}+8a^{2}+13a-8$ |
| 41.3-d1 |
41.3-d |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41^{7} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1358.459986$ |
1.61963 |
\( -\frac{208407593862926594044}{194754273881} a^{5} + \frac{141658003656526461242}{194754273881} a^{4} + \frac{1229066730164612970543}{194754273881} a^{3} - \frac{16335768573744324071}{4750104241} a^{2} - \frac{1301096988038281036921}{194754273881} a + \frac{157850815853926536686}{194754273881} \) |
\( \bigl[a^{2} - 1\) , \( -a^{5} + 7 a^{3} - a^{2} - 9 a + 2\) , \( 0\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 8 a^{2} - 10 a + 9\) , \( 7 a^{5} - 32 a^{3} + 11 a^{2} + 23 a - 4\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{5}+7a^{3}-a^{2}-9a+2\right){x}^{2}+\left(-a^{5}+2a^{4}+7a^{3}-8a^{2}-10a+9\right){x}+7a^{5}-32a^{3}+11a^{2}+23a-4$ |
| 41.3-e1 |
41.3-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41^{3} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.246297662$ |
$17427.30765$ |
2.55877 |
\( -\frac{1132366102}{68921} a^{5} + \frac{1515352091}{68921} a^{4} + \frac{6136409687}{68921} a^{3} - \frac{199753741}{1681} a^{2} - \frac{4705520957}{68921} a + \frac{6304165628}{68921} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 10 a - 2\) , \( -3 a^{5} + 2 a^{4} + 17 a^{3} - 10 a^{2} - 15 a + 2\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 10 a - 3\) , \( 2 a^{4} + 3 a^{3} - 5 a^{2} - 6 a\) , \( -7 a^{5} + 9 a^{4} + 47 a^{3} - 35 a^{2} - 55 a + 6\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+6a^{2}+10a-2\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+10a-3\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+17a^{3}-10a^{2}-15a+2\right){x}^{2}+\left(2a^{4}+3a^{3}-5a^{2}-6a\right){x}-7a^{5}+9a^{4}+47a^{3}-35a^{2}-55a+6$ |
| 41.3-e2 |
41.3-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( - 41^{6} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.492595325$ |
$4356.826913$ |
2.55877 |
\( -\frac{3868146036397569720}{4750104241} a^{5} + \frac{7289390284716297722}{4750104241} a^{4} + \frac{20185766230579865977}{4750104241} a^{3} - \frac{980914258788784182}{115856201} a^{2} - \frac{12396489983066410677}{4750104241} a + \frac{33384677007660926967}{4750104241} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 10 a - 2\) , \( -3 a^{5} + 2 a^{4} + 17 a^{3} - 10 a^{2} - 15 a + 2\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 10 a - 3\) , \( -70 a^{5} + 52 a^{4} + 413 a^{3} - 240 a^{2} - 431 a + 50\) , \( -248 a^{5} + 166 a^{4} + 1478 a^{3} - 780 a^{2} - 1603 a + 192\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+6a^{2}+10a-2\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+10a-3\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+17a^{3}-10a^{2}-15a+2\right){x}^{2}+\left(-70a^{5}+52a^{4}+413a^{3}-240a^{2}-431a+50\right){x}-248a^{5}+166a^{4}+1478a^{3}-780a^{2}-1603a+192$ |
| 41.3-e3 |
41.3-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41 \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$0.738892988$ |
$23.90577181$ |
2.55877 |
\( -\frac{2734619766578096}{41} a^{5} + \frac{5127716296916528}{41} a^{4} + \frac{14279351126657144}{41} a^{3} - 689869752856215 a^{2} - \frac{8804507911543798}{41} a + \frac{23455352094983401}{41} \) |
\( \bigl[a^{5} - 6 a^{3} + 8 a + 2\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 2 a + 2\) , \( a^{2} - 2\) , \( -114 a^{5} + 45 a^{4} + 697 a^{3} - 169 a^{2} - 813 a - 140\) , \( -618 a^{5} + 161 a^{4} + 3799 a^{3} - 440 a^{2} - 4532 a - 1239\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+8a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-9a^{2}-2a+2\right){x}^{2}+\left(-114a^{5}+45a^{4}+697a^{3}-169a^{2}-813a-140\right){x}-618a^{5}+161a^{4}+3799a^{3}-440a^{2}-4532a-1239$ |
| 41.3-e4 |
41.3-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( - 41^{2} \) |
$102.13324$ |
$(a^3-a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$1.477785976$ |
$5.976442953$ |
2.55877 |
\( -\frac{59985851336154346732878490305700}{1681} a^{5} + \frac{113019715254194002660867511068820}{1681} a^{4} + \frac{313027539374854203747394355382504}{1681} a^{3} - \frac{15208937025256991952350710659544}{41} a^{2} - \frac{192239175684393217825484451013707}{1681} a + \frac{517593336136737221171637388394509}{1681} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 4 a^{2} + 9 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 6 a^{2} + 4 a - 3\) , \( 183 a^{5} - 297 a^{4} - 948 a^{3} + 1709 a^{2} + 549 a - 1692\) , \( 2440 a^{5} - 5092 a^{4} - 12258 a^{3} + 28901 a^{2} + 5669 a - 26972\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+17a-2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+6a^{2}+4a-3\right){y}={x}^{3}+\left(2a^{5}-a^{4}-11a^{3}+4a^{2}+9a+1\right){x}^{2}+\left(183a^{5}-297a^{4}-948a^{3}+1709a^{2}+549a-1692\right){x}+2440a^{5}-5092a^{4}-12258a^{3}+28901a^{2}+5669a-26972$ |
| 41.4-a1 |
41.4-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41^{5} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6510.954223$ |
1.94068 |
\( -\frac{111795332208180804}{115856201} a^{5} + \frac{54644123139141956}{115856201} a^{4} + \frac{641562038225938648}{115856201} a^{3} - \frac{260220358529917204}{115856201} a^{2} - \frac{616867665124371048}{115856201} a + \frac{73976389687605349}{115856201} \) |
\( \bigl[a\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 4\) , \( a^{2} + a - 2\) , \( -2 a^{5} + 13 a^{3} - 9 a^{2} - 11 a + 7\) , \( -4 a^{5} + 3 a^{4} + 10 a^{3} - 3 a^{2} - 7 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a-4\right){x}^{2}+\left(-2a^{5}+13a^{3}-9a^{2}-11a+7\right){x}-4a^{5}+3a^{4}+10a^{3}-3a^{2}-7a-2$ |
| 41.4-a2 |
41.4-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41^{10} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$813.8692778$ |
1.94068 |
\( -\frac{1745139273055731148197952}{13422659310152401} a^{5} + \frac{3373227824416182197653522}{13422659310152401} a^{4} + \frac{8846215934494906178049104}{13422659310152401} a^{3} - \frac{18077979504508233993782986}{13422659310152401} a^{2} - \frac{5322436363201050502227782}{13422659310152401} a + \frac{14959775970217750942840429}{13422659310152401} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 11 a - 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 2 a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 6 a^{2} + 6 a - 4\) , \( 36 a^{5} - 20 a^{4} - 199 a^{3} + 92 a^{2} + 184 a - 31\) , \( -102 a^{5} + 51 a^{4} + 576 a^{3} - 221 a^{2} - 549 a + 38\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+11a-1\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+6a^{2}+6a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-9a^{2}-2a+3\right){x}^{2}+\left(36a^{5}-20a^{4}-199a^{3}+92a^{2}+184a-31\right){x}-102a^{5}+51a^{4}+576a^{3}-221a^{2}-549a+38$ |
| 41.4-b1 |
41.4-b |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41 \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$4678.254988$ |
1.39442 |
\( \frac{132422900}{41} a^{5} - \frac{141704392}{41} a^{4} - \frac{798145247}{41} a^{3} + \frac{689842493}{41} a^{2} + \frac{906291495}{41} a - \frac{237335216}{41} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( -6 a^{5} + 5 a^{4} + 34 a^{3} - 23 a^{2} - 33 a + 4\) , \( -6 a^{5} + 3 a^{4} + 36 a^{3} - 15 a^{2} - 43 a + 5\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-4\right){x}{y}+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+17a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-4a^{2}-3a-1\right){x}^{2}+\left(-6a^{5}+5a^{4}+34a^{3}-23a^{2}-33a+4\right){x}-6a^{5}+3a^{4}+36a^{3}-15a^{2}-43a+5$ |
| 41.4-b2 |
41.4-b |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( - 41^{2} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$584.7818735$ |
1.39442 |
\( -\frac{46785115689974520}{1681} a^{5} + \frac{25523470799745310}{1681} a^{4} + \frac{267495305548152369}{1681} a^{3} - \frac{124251905123044313}{1681} a^{2} - \frac{253745891578685595}{1681} a + \frac{46114837230979857}{1681} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( 19 a^{5} - 10 a^{4} - 106 a^{3} + 47 a^{2} + 92 a - 16\) , \( 55 a^{5} - 29 a^{4} - 312 a^{3} + 137 a^{2} + 286 a - 40\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-4\right){x}{y}+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+17a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-4a^{2}-3a-1\right){x}^{2}+\left(19a^{5}-10a^{4}-106a^{3}+47a^{2}+92a-16\right){x}+55a^{5}-29a^{4}-312a^{3}+137a^{2}+286a-40$ |
| 41.4-c1 |
41.4-c |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41 \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1351.437236$ |
1.61126 |
\( \frac{125711789726}{41} a^{5} - \frac{61449523288}{41} a^{4} - \frac{721420682984}{41} a^{3} + \frac{292627885035}{41} a^{2} + \frac{693639106205}{41} a - \frac{83187425920}{41} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 8 a\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 10 a^{2} - 10 a + 4\) , \( a + 1\) , \( 5 a^{5} - a^{4} - 27 a^{3} + 8 a^{2} + 26 a - 1\) , \( -a^{5} + 4 a^{4} + 10 a^{3} - 14 a^{2} - 14 a + 4\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+8a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+11a^{3}-10a^{2}-10a+4\right){x}^{2}+\left(5a^{5}-a^{4}-27a^{3}+8a^{2}+26a-1\right){x}-a^{5}+4a^{4}+10a^{3}-14a^{2}-14a+4$ |
| 41.4-d1 |
41.4-d |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41^{7} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1358.459986$ |
1.61963 |
\( \frac{2193085400250940456}{194754273881} a^{5} - \frac{9040335834589460238}{194754273881} a^{4} + \frac{8220320611440950985}{194754273881} a^{3} + \frac{6678172413832281891}{194754273881} a^{2} - \frac{9786903378511537191}{194754273881} a + \frac{1033336974108669203}{194754273881} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 13 a - 2\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 11 a^{2} - 9 a + 5\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 16 a^{2} - 7 a + 14\) , \( -6 a^{5} + 16 a^{4} + 27 a^{3} - 92 a^{2} - 3 a + 86\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+6a^{2}+13a-2\right){x}{y}+\left(a^{5}-6a^{3}+8a+2\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+11a^{3}-11a^{2}-9a+5\right){x}^{2}+\left(-2a^{5}+3a^{4}+10a^{3}-16a^{2}-7a+14\right){x}-6a^{5}+16a^{4}+27a^{3}-92a^{2}-3a+86$ |
| 41.4-e1 |
41.4-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( - 41^{2} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$1.477785976$ |
$5.976442953$ |
2.55877 |
\( \frac{36649377214722269688376981404391}{1681} a^{5} + \frac{4804213580822606147447044113221}{1681} a^{4} - \frac{173008694646261741480385301974650}{1681} a^{3} + \frac{34446773860453626004806361131099}{1681} a^{2} + \frac{146707785669385287322288443886585}{1681} a - \frac{17197513544561278871243743300424}{1681} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 10 a - 3\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 10 a^{2} - a + 6\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 1\) , \( 78 a^{5} - 247 a^{4} + 122 a^{3} + 129 a^{2} - 104 a + 23\) , \( 2279 a^{5} - 9254 a^{4} + 8032 a^{3} + 6740 a^{2} - 9382 a + 993\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+6a^{2}+10a-3\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-10a^{2}-a+6\right){x}^{2}+\left(78a^{5}-247a^{4}+122a^{3}+129a^{2}-104a+23\right){x}+2279a^{5}-9254a^{4}+8032a^{3}+6740a^{2}-9382a+993$ |
| 41.4-e2 |
41.4-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41 \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$0.738892988$ |
$23.90577181$ |
2.55877 |
\( \frac{1661681620471232}{41} a^{5} + \frac{213704000156457}{41} a^{4} - \frac{7841722250015960}{41} a^{3} + \frac{1577558381739890}{41} a^{2} + \frac{6635361185868735}{41} a - \frac{778052671995566}{41} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 7 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 5\) , \( -30 a^{5} + 3 a^{4} + 169 a^{3} - 71 a^{2} - 156 a + 28\) , \( -115 a^{5} - 28 a^{4} + 635 a^{3} - 157 a^{2} - 561 a + 63\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a-1\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+11a^{2}+9a-5\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-7a+4\right){x}^{2}+\left(-30a^{5}+3a^{4}+169a^{3}-71a^{2}-156a+28\right){x}-115a^{5}-28a^{4}+635a^{3}-157a^{2}-561a+63$ |
| 41.4-e3 |
41.4-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( - 41^{6} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.492595325$ |
$4356.826913$ |
2.55877 |
\( \frac{2361415517723691336}{4750104241} a^{5} + \frac{312405531641926157}{4750104241} a^{4} - \frac{11145383118536595673}{4750104241} a^{3} + \frac{2208505528549032067}{4750104241} a^{2} + \frac{9451172168707485868}{4750104241} a - \frac{1100146408697507811}{4750104241} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 7 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 5\) , \( -5 a^{5} - 2 a^{4} + 29 a^{3} - a^{2} - 31 a - 2\) , \( -10 a^{5} - 2 a^{4} + 55 a^{3} - 13 a^{2} - 49 a + 5\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a-1\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+11a^{2}+9a-5\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-7a+4\right){x}^{2}+\left(-5a^{5}-2a^{4}+29a^{3}-a^{2}-31a-2\right){x}-10a^{5}-2a^{4}+55a^{3}-13a^{2}-49a+5$ |
| 41.4-e4 |
41.4-e |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41^{3} \) |
$102.13324$ |
$(a^5-a^4-6a^3+4a^2+7a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.246297662$ |
$17427.30765$ |
2.55877 |
\( \frac{540166855}{68921} a^{5} - \frac{112536867}{68921} a^{4} - \frac{2583214205}{68921} a^{3} + \frac{1175827261}{68921} a^{2} + \frac{1962941452}{68921} a - \frac{284998027}{68921} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 7 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 5\) , \( -5 a^{5} + 3 a^{4} + 29 a^{3} - 16 a^{2} - 31 a + 8\) , \( -a^{5} + 6 a^{3} - a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a-1\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+11a^{2}+9a-5\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-6a^{2}-7a+4\right){x}^{2}+\left(-5a^{5}+3a^{4}+29a^{3}-16a^{2}-31a+8\right){x}-a^{5}+6a^{3}-a^{2}-6a-2$ |
| 64.1-a1 |
64.1-a |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{6} \) |
$105.99453$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1363.207533$ |
1.62530 |
\( 146989275419572 a^{5} - \frac{143700390471519}{2} a^{4} - 843525494076395 a^{3} + \frac{684313694606955}{2} a^{2} + 811041701707335 a - \frac{194534795299797}{2} \) |
\( \bigl[a^{5} - 6 a^{3} + 8 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 7 a - 1\) , \( -4 a^{5} + 2 a^{4} + 23 a^{3} - 12 a^{2} - 22 a + 3\) , \( -7 a^{5} + 4 a^{4} + 39 a^{3} - 20 a^{2} - 41 a + 5\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+8a+1\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+7a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-5a^{2}-7a+2\right){x}^{2}+\left(-4a^{5}+2a^{4}+23a^{3}-12a^{2}-22a+3\right){x}-7a^{5}+4a^{4}+39a^{3}-20a^{2}-41a+5$ |
| 64.1-b1 |
64.1-b |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{18} \) |
$105.99453$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.007393886$ |
$19202.85666$ |
3.04706 |
\( -\frac{4155719}{8} a^{5} - \frac{2581671}{8} a^{4} + \frac{16657899}{8} a^{3} + \frac{900641}{4} a^{2} - 1374892 a + \frac{1236175}{8} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 6 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 10 a^{2} + 2 a - 5\) , \( a^{5} - a^{4} - 5 a^{3} + 6 a^{2} + 3 a - 3\) , \( a^{5} + 2 a^{4} - 6 a^{3} - 13 a^{2} + 7 a + 18\) , \( -11 a^{5} + 2 a^{4} + 64 a^{3} - 8 a^{2} - 66 a - 8\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+6a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+6a^{2}+3a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+10a^{2}+2a-5\right){x}^{2}+\left(a^{5}+2a^{4}-6a^{3}-13a^{2}+7a+18\right){x}-11a^{5}+2a^{4}+64a^{3}-8a^{2}-66a-8$ |
| 64.1-c1 |
64.1-c |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{18} \) |
$105.99453$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.007393886$ |
$19202.85666$ |
3.04706 |
\( 1361559 a^{5} - 2557565 a^{4} - \frac{57078417}{8} a^{3} + \frac{113409673}{8} a^{2} + 4389277 a - \frac{94213565}{8} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 6 a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 11 a^{2} + 16 a - 4\) , \( 2 a^{4} - 9 a^{2} + 3 a + 6\) , \( -2 a^{4} + 4 a^{3} + 8 a^{2} - 17 a + 4\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+6a-1\right){x}{y}+\left(3a^{5}-2a^{4}-17a^{3}+11a^{2}+16a-4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(2a^{4}-9a^{2}+3a+6\right){x}-2a^{4}+4a^{3}+8a^{2}-17a+4$ |
| 64.1-d1 |
64.1-d |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{6} \) |
$105.99453$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1363.207533$ |
1.62530 |
\( -\frac{20074120848835}{2} a^{5} + 29671853291873 a^{4} + 21812204105468 a^{3} - 131265137584045 a^{2} + 105445461314860 a - 10496500642032 \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a\) , \( -a^{5} + 5 a^{3} - 4 a - 1\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a\) , \( -2 a^{4} + 10 a^{2} - 2 a - 10\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 3 a - 9\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-4a-1\right){x}^{2}+\left(-2a^{4}+10a^{2}-2a-10\right){x}-2a^{4}+a^{3}+9a^{2}-3a-9$ |
| 71.1-a1 |
71.1-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( -71 \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7524.719829$ |
2.24285 |
\( \frac{89431847697}{71} a^{5} - \frac{43715369081}{71} a^{4} - \frac{513221401647}{71} a^{3} + \frac{208176406233}{71} a^{2} + \frac{493457568669}{71} a - \frac{59179686201}{71} \) |
\( \bigl[a^{5} - 6 a^{3} + 8 a + 1\) , \( -a^{5} + 7 a^{3} - 10 a\) , \( 0\) , \( -a^{5} - a^{4} + 6 a^{3} + 3 a^{2} - 10 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+8a+1\right){x}{y}={x}^{3}+\left(-a^{5}+7a^{3}-10a\right){x}^{2}+\left(-a^{5}-a^{4}+6a^{3}+3a^{2}-10a+1\right){x}$ |
| 71.1-a2 |
71.1-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{2} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$940.5899787$ |
2.24285 |
\( -\frac{11839647554558478959841}{5041} a^{5} + \frac{5787367720309411887888}{5041} a^{4} + \frac{67944035529605585955853}{5041} a^{3} - \frac{27559945908517340113981}{5041} a^{2} - \frac{65327540866640073976839}{5041} a + \frac{7834664827885457662413}{5041} \) |
\( \bigl[a^{5} - 6 a^{3} + 8 a + 1\) , \( -a^{5} + 7 a^{3} - 10 a\) , \( 0\) , \( 4 a^{5} + 4 a^{4} - 24 a^{3} - 12 a^{2} + 40 a - 4\) , \( 18 a^{5} + 27 a^{4} - 107 a^{3} - 80 a^{2} + 191 a - 21\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+8a+1\right){x}{y}={x}^{3}+\left(-a^{5}+7a^{3}-10a\right){x}^{2}+\left(4a^{5}+4a^{4}-24a^{3}-12a^{2}+40a-4\right){x}+18a^{5}+27a^{4}-107a^{3}-80a^{2}+191a-21$ |
| 71.1-b1 |
71.1-b |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.012503843$ |
$34628.08642$ |
3.09737 |
\( -\frac{2239709172}{71} a^{5} + \frac{1484198416}{71} a^{4} + \frac{13230268318}{71} a^{3} - \frac{6970381746}{71} a^{2} - \frac{14079872535}{71} a + \frac{1447849626}{71} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 11 a^{2} + 16 a - 4\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 11 a^{2} - 8 a + 5\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 1\) , \( a^{5} - 6 a^{4} - 3 a^{3} + 36 a^{2} - 8 a - 37\) , \( -5 a^{5} + 11 a^{4} + 26 a^{3} - 60 a^{2} - 14 a + 49\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+11a^{2}+16a-4\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-1\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+11a^{3}-11a^{2}-8a+5\right){x}^{2}+\left(a^{5}-6a^{4}-3a^{3}+36a^{2}-8a-37\right){x}-5a^{5}+11a^{4}+26a^{3}-60a^{2}-14a+49$ |
| 71.1-c1 |
71.1-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{9} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$76.19196661$ |
1.83952 |
\( \frac{15074510965293950172967777821274}{45848500718449031} a^{5} - \frac{10246376051394215233897656562451}{45848500718449031} a^{4} - \frac{88900688178482615252690302298347}{45848500718449031} a^{3} + \frac{48445404031931088186318067724029}{45848500718449031} a^{2} + \frac{94110746850176071444600453149653}{45848500718449031} a - \frac{11417621517279237044933795673020}{45848500718449031} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 3 a - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 9 a - 4\) , \( a^{2} + a - 1\) , \( -15 a^{5} - 9 a^{4} + 70 a^{3} + 20 a^{2} - 72 a - 28\) , \( -111 a^{5} - 50 a^{4} + 481 a^{3} - 2 a^{2} - 394 a - 1\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+3a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-9a-4\right){x}^{2}+\left(-15a^{5}-9a^{4}+70a^{3}+20a^{2}-72a-28\right){x}-111a^{5}-50a^{4}+481a^{3}-2a^{2}-394a-1$ |
| 71.1-c2 |
71.1-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{3} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$55543.94366$ |
1.83952 |
\( -\frac{29169505440}{357911} a^{5} + \frac{151117918400}{357911} a^{4} - \frac{25425543508}{357911} a^{3} - \frac{654677096029}{357911} a^{2} + \frac{727216594590}{357911} a - \frac{74279894665}{357911} \) |
\( \bigl[a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 10 a - 2\) , \( a^{2} - 2\) , \( -a^{4} + 3 a^{2} + 1\) , \( -7 a^{5} + 5 a^{4} + 39 a^{3} - 20 a^{2} - 41 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-11a^{3}+9a^{2}+10a-2\right){x}^{2}+\left(-a^{4}+3a^{2}+1\right){x}-7a^{5}+5a^{4}+39a^{3}-20a^{2}-41a+4$ |
| 71.1-c3 |
71.1-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{18} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$324$ |
\( 2 \) |
$1$ |
$9.523995827$ |
1.83952 |
\( -\frac{32384932030645477671104879759286297815174}{2102085018129621311776010144838961} a^{5} + \frac{21844148113879633966889059724712269539776}{2102085018129621311776010144838961} a^{4} + \frac{190860263774172764626726183633974666350953}{2102085018129621311776010144838961} a^{3} - \frac{103295526582756225572298575973860225748056}{2102085018129621311776010144838961} a^{2} - \frac{201599340834596793007844079193785826495439}{2102085018129621311776010144838961} a + \frac{24448457916825108615003230495913550870705}{2102085018129621311776010144838961} \) |
\( \bigl[a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 10 a - 2\) , \( a^{2} - 2\) , \( -165 a^{5} + 124 a^{4} + 1015 a^{3} - 622 a^{2} - 1135 a + 136\) , \( -2020 a^{5} + 1467 a^{4} + 12003 a^{3} - 6970 a^{2} - 13017 a + 1579\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-11a^{3}+9a^{2}+10a-2\right){x}^{2}+\left(-165a^{5}+124a^{4}+1015a^{3}-622a^{2}-1135a+136\right){x}-2020a^{5}+1467a^{4}+12003a^{3}-6970a^{2}-13017a+1579$ |
| 71.1-c4 |
71.1-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{6} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$6942.992958$ |
1.83952 |
\( \frac{66054493429974005697994}{128100283921} a^{5} - \frac{195272188967789233216758}{128100283921} a^{4} - \frac{143547654652558570361494}{128100283921} a^{3} + \frac{863864093776112345760668}{128100283921} a^{2} - \frac{693943093157691876933631}{128100283921} a + \frac{69078108932255278893563}{128100283921} \) |
\( \bigl[a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 10 a - 2\) , \( a^{2} - 2\) , \( 10 a^{5} - 11 a^{4} - 45 a^{3} + 28 a^{2} + 45 a - 4\) , \( -16 a^{5} + 45 a^{4} - a^{3} - 49 a^{2} + 6 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-11a^{3}+9a^{2}+10a-2\right){x}^{2}+\left(10a^{5}-11a^{4}-45a^{3}+28a^{2}+45a-4\right){x}-16a^{5}+45a^{4}-a^{3}-49a^{2}+6a-1$ |
| 71.1-d1 |
71.1-d |
$2$ |
$5$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$0.220956997$ |
$41839.53297$ |
2.64531 |
\( \frac{1061831}{71} a^{5} - \frac{19223}{71} a^{4} - \frac{5239532}{71} a^{3} + \frac{1358533}{71} a^{2} + \frac{4577495}{71} a - \frac{444281}{71} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( a^{5} - 5 a^{3} - a^{2} + 4 a + 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 14 a - 3\) , \( -4 a^{5} + 3 a^{4} + 22 a^{3} - 14 a^{2} - 21 a + 8\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 12 a^{2} - 8 a + 5\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-4\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+6a^{2}+14a-3\right){y}={x}^{3}+\left(a^{5}-5a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-4a^{5}+3a^{4}+22a^{3}-14a^{2}-21a+8\right){x}-2a^{5}+2a^{4}+11a^{3}-12a^{2}-8a+5$ |
| 71.1-d2 |
71.1-d |
$2$ |
$5$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71^{5} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 5 \) |
$1.104784988$ |
$2.677730110$ |
2.64531 |
\( \frac{87005242380951413447981}{1804229351} a^{5} - \frac{358352300293503552738053}{1804229351} a^{4} + \frac{324582348954291382628292}{1804229351} a^{3} + \frac{267564005100390507857116}{1804229351} a^{2} - \frac{389861672438050834540672}{1804229351} a + \frac{41146371824560894280341}{1804229351} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 6 a - 1\) , \( -a^{5} + 5 a^{3} - a^{2} - 4 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 1\) , \( -36 a^{5} - 27 a^{4} + 166 a^{3} + 15 a^{2} - 135 a - 7\) , \( -39 a^{5} - 341 a^{4} - 159 a^{3} + 650 a^{2} + 393 a - 108\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+6a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-36a^{5}-27a^{4}+166a^{3}+15a^{2}-135a-7\right){x}-39a^{5}-341a^{4}-159a^{3}+650a^{2}+393a-108$ |
| 71.1-e1 |
71.1-e |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71^{5} \) |
$106.91533$ |
$(-2a^5+a^4+12a^3-4a^2-12a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$866.1300830$ |
1.03265 |
\( -\frac{124315078720314611694730}{1804229351} a^{5} + \frac{84498863776551023357538}{1804229351} a^{4} + \frac{733137948754350072437846}{1804229351} a^{3} - \frac{399515065412184994079968}{1804229351} a^{2} - \frac{776103776934549949304354}{1804229351} a + \frac{94157783375202703558381}{1804229351} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 11 a^{2} + 16 a - 5\) , \( -a^{5} + 7 a^{3} + a^{2} - 9 a - 3\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a\) , \( -69 a^{5} + 47 a^{4} + 407 a^{3} - 221 a^{2} - 427 a + 54\) , \( -236 a^{5} + 160 a^{4} + 1392 a^{3} - 756 a^{2} - 1470 a + 178\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+11a^{2}+16a-5\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-9a-3\right){x}^{2}+\left(-69a^{5}+47a^{4}+407a^{3}-221a^{2}-427a+54\right){x}-236a^{5}+160a^{4}+1392a^{3}-756a^{2}-1470a+178$ |
| 71.2-a1 |
71.2-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( -71 \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7524.719829$ |
2.24285 |
\( -\frac{6106826263}{71} a^{5} + \frac{18053181172}{71} a^{4} + \frac{13271273043}{71} a^{3} - 1124865728 a^{2} + \frac{64155393460}{71} a - \frac{6385724079}{71} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a\) , \( a^{3} - 4 a\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -4 a^{4} + 3 a^{3} + 24 a^{2} - 13 a - 26\) , \( -6 a^{5} + 11 a^{4} + 32 a^{3} - 60 a^{2} - 22 a + 48\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a-1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-4a^{4}+3a^{3}+24a^{2}-13a-26\right){x}-6a^{5}+11a^{4}+32a^{3}-60a^{2}-22a+48$ |
| 71.2-a2 |
71.2-a |
$2$ |
$2$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{2} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$940.5899787$ |
2.24285 |
\( \frac{808462120758107459268}{5041} a^{5} - \frac{2389999464232167402569}{5041} a^{4} - \frac{1756922926803356952415}{5041} a^{3} + \frac{148916966593396023766}{71} a^{2} - \frac{8493388913885282041853}{5041} a + \frac{845468825674899153375}{5041} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a\) , \( a^{3} - 4 a\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( 15 a^{5} + a^{4} - 87 a^{3} - 11 a^{2} + 87 a + 29\) , \( 22 a^{5} + 32 a^{4} - 142 a^{3} - 195 a^{2} + 192 a + 226\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a-1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(15a^{5}+a^{4}-87a^{3}-11a^{2}+87a+29\right){x}+22a^{5}+32a^{4}-142a^{3}-195a^{2}+192a+226$ |
| 71.2-b1 |
71.2-b |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( 71 \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.012503843$ |
$34628.08642$ |
3.09737 |
\( \frac{3525241}{71} a^{5} - \frac{100438949}{71} a^{4} + \frac{186835268}{71} a^{3} + 726541 a^{2} - \frac{189655515}{71} a + \frac{21559677}{71} \) |
\( \bigl[a^{5} - 6 a^{3} + a^{2} + 7 a\) , \( -a^{5} + 5 a^{3} - 3 a - 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 6\) , \( -2 a^{5} - a^{4} + 15 a^{3} - 4 a^{2} - 14 a + 4\) , \( -a^{5} + 2 a^{4} - a^{3} + 3 a^{2} + a - 6\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+a^{2}+7a\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+11a^{2}+9a-6\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-3a-1\right){x}^{2}+\left(-2a^{5}-a^{4}+15a^{3}-4a^{2}-14a+4\right){x}-a^{5}+2a^{4}-a^{3}+3a^{2}+a-6$ |
| 71.2-c1 |
71.2-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{9} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$76.19196661$ |
1.83952 |
\( -\frac{158630922266261756910869723443}{45848500718449031} a^{5} + \frac{653911997844922927694411264743}{45848500718449031} a^{4} - \frac{594592079683515243651146288639}{45848500718449031} a^{3} - \frac{6803996678656713454955510359}{645753531245761} a^{2} + \frac{707949397468455161594658237456}{45848500718449031} a - \frac{74747559645007814527976608685}{45848500718449031} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 11 a\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 4 a^{2} + 9 a + 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 1\) , \( -a^{5} + 18 a^{4} - 15 a^{3} - 76 a^{2} + 107 a - 18\) , \( -115 a^{5} + 350 a^{4} + 242 a^{3} - 1547 a^{2} + 1282 a - 151\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+11a\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+13a-1\right){y}={x}^{3}+\left(2a^{5}-a^{4}-11a^{3}+4a^{2}+9a+2\right){x}^{2}+\left(-a^{5}+18a^{4}-15a^{3}-76a^{2}+107a-18\right){x}-115a^{5}+350a^{4}+242a^{3}-1547a^{2}+1282a-151$ |
| 71.2-c2 |
71.2-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{3} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$55543.94366$ |
1.83952 |
\( \frac{795468305268}{357911} a^{5} - \frac{372164820189}{357911} a^{4} - \frac{4572367255460}{357911} a^{3} + \frac{24787487394}{5041} a^{2} + \frac{4415828102417}{357911} a - \frac{437325406162}{357911} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 16 a - 2\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 4 a^{2} + 9 a + 2\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 1\) , \( 7 a^{5} - 14 a^{4} - 35 a^{3} + 73 a^{2} + 15 a - 49\) , \( -9 a^{5} + 17 a^{4} + 48 a^{3} - 97 a^{2} - 34 a + 89\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+16a-2\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a-1\right){y}={x}^{3}+\left(2a^{5}-a^{4}-11a^{3}+4a^{2}+9a+2\right){x}^{2}+\left(7a^{5}-14a^{4}-35a^{3}+73a^{2}+15a-49\right){x}-9a^{5}+17a^{4}+48a^{3}-97a^{2}-34a+89$ |
| 71.2-c3 |
71.2-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{18} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$324$ |
\( 2 \) |
$1$ |
$9.523995827$ |
1.83952 |
\( \frac{359759544497203929509210595811801196108}{2102085018129621311776010144838961} a^{5} - \frac{1526001064921001971675213058941586980591}{2102085018129621311776010144838961} a^{4} + \frac{1290771142716877822847831346872313363443}{2102085018129621311776010144838961} a^{3} + \frac{24011145605113599946892149929673421861}{29606831241262271996845213307591} a^{2} - \frac{2258719519482491188111758284764967278838}{2102085018129621311776010144838961} a + \frac{237279529375170571900032808388074634821}{2102085018129621311776010144838961} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 16 a - 2\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 4 a^{2} + 9 a + 2\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 1\) , \( -53 a^{5} + 106 a^{4} + 230 a^{3} - 537 a^{2} + 35 a + 241\) , \( 610 a^{5} - 1030 a^{4} - 3660 a^{3} + 6180 a^{2} + 4069 a - 7058\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+16a-2\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a-1\right){y}={x}^{3}+\left(2a^{5}-a^{4}-11a^{3}+4a^{2}+9a+2\right){x}^{2}+\left(-53a^{5}+106a^{4}+230a^{3}-537a^{2}+35a+241\right){x}+610a^{5}-1030a^{4}-3660a^{3}+6180a^{2}+4069a-7058$ |
| 71.2-c4 |
71.2-c |
$4$ |
$6$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{6} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$6942.992958$ |
1.83952 |
\( -\frac{967341991986971198130709}{128100283921} a^{5} + \frac{472848139459036686462353}{128100283921} a^{4} + \frac{5551272645994541724957784}{128100283921} a^{3} - \frac{31714702059610557915333}{1804229351} a^{2} - \frac{5337493446250041016849779}{128100283921} a + \frac{640120070053873724512754}{128100283921} \) |
\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 16 a - 2\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 4 a^{2} + 9 a + 2\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 1\) , \( 2 a^{5} - 4 a^{4} - 10 a^{3} + 23 a^{2} + 5 a - 24\) , \( -34 a^{5} + 57 a^{4} + 180 a^{3} - 312 a^{2} - 119 a + 251\bigr] \) |
${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+16a-2\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a-1\right){y}={x}^{3}+\left(2a^{5}-a^{4}-11a^{3}+4a^{2}+9a+2\right){x}^{2}+\left(2a^{5}-4a^{4}-10a^{3}+23a^{2}+5a-24\right){x}-34a^{5}+57a^{4}+180a^{3}-312a^{2}-119a+251$ |
| 71.2-d1 |
71.2-d |
$2$ |
$5$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( 71 \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$0.220956997$ |
$41839.53297$ |
2.64531 |
\( -\frac{1497412}{71} a^{5} + \frac{2670984}{71} a^{4} + \frac{7853018}{71} a^{3} - 205878 a^{2} - \frac{4974801}{71} a + \frac{11806486}{71} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 12 a - 2\) , \( a^{5} - 6 a^{3} + 7 a + 1\) , \( 5 a^{5} - a^{4} - 35 a^{3} + 15 a^{2} + 37 a - 5\) , \( 6 a^{4} - 17 a^{3} + a^{2} + 19 a - 3\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a-1\right){x}{y}+\left(a^{5}-6a^{3}+7a+1\right){y}={x}^{3}+\left(2a^{5}-a^{4}-12a^{3}+6a^{2}+12a-2\right){x}^{2}+\left(5a^{5}-a^{4}-35a^{3}+15a^{2}+37a-5\right){x}+6a^{4}-17a^{3}+a^{2}+19a-3$ |
| 71.2-d2 |
71.2-d |
$2$ |
$5$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( 71^{5} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 5 \) |
$1.104784988$ |
$2.677730110$ |
2.64531 |
\( -\frac{8247140304222094965493077}{1804229351} a^{5} + \frac{5604981946702415707053678}{1804229351} a^{4} + \frac{48636228022092569929642284}{1804229351} a^{3} - \frac{373249468128802130696271}{25411681} a^{2} - \frac{51484454114041041875459375}{1804229351} a + \frac{6246122724889555548708106}{1804229351} \) |
\( \bigl[a^{5} - 6 a^{3} + 7 a + 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 10 a^{2} - 3 a + 5\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( 28 a^{5} + 26 a^{4} - 270 a^{3} - 34 a^{2} + 644 a - 382\) , \( -3268 a^{5} + 10236 a^{4} + 5766 a^{3} - 44568 a^{2} + 40342 a - 6860\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+7a+1\right){x}{y}+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-10a^{2}-3a+5\right){x}^{2}+\left(28a^{5}+26a^{4}-270a^{3}-34a^{2}+644a-382\right){x}-3268a^{5}+10236a^{4}+5766a^{3}-44568a^{2}+40342a-6860$ |
| 71.2-e1 |
71.2-e |
$1$ |
$1$ |
6.6.703493.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( 71^{5} \) |
$106.91533$ |
$(-3a^5+2a^4+17a^3-9a^2-15a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$866.1300830$ |
1.03265 |
\( \frac{1308182862487508633234}{1804229351} a^{5} - \frac{5392620768143376532170}{1804229351} a^{4} + \frac{4903426392612545931130}{1804229351} a^{3} + \frac{56110568593616337368}{25411681} a^{2} - \frac{5838251061832125300750}{1804229351} a + \frac{616421267153033327191}{1804229351} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 11 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 2 a - 2\) , \( a^{5} - 6 a^{3} + 8 a + 1\) , \( 38 a^{5} - 67 a^{4} - 196 a^{3} + 362 a^{2} + 113 a - 275\) , \( -200 a^{5} + 382 a^{4} + 1049 a^{3} - 2118 a^{2} - 663 a + 1796\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+11a-1\right){x}{y}+\left(a^{5}-6a^{3}+8a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+2a-2\right){x}^{2}+\left(38a^{5}-67a^{4}-196a^{3}+362a^{2}+113a-275\right){x}-200a^{5}+382a^{4}+1049a^{3}-2118a^{2}-663a+1796$ |
*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.
