| 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 |
$2$ |
$7$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$117.85504$ |
$(a^3-a^2-2a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$86211.57618$ |
1.65192 |
\( \frac{124200}{13} a^{5} - \frac{154732}{13} a^{4} - \frac{604704}{13} a^{3} + \frac{256238}{13} a^{2} + \frac{701798}{13} a + \frac{201965}{13} \) |
\( \bigl[a\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + 2 a + 4\) , \( 6 a^{5} - 16 a^{4} - 15 a^{3} + 48 a^{2} - 23\) , \( -3 a^{5} + 9 a^{4} + 5 a^{3} - 27 a^{2} + 6 a + 12\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+2a+4\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+3\right){x}^{2}+\left(6a^{5}-16a^{4}-15a^{3}+48a^{2}-23\right){x}-3a^{5}+9a^{4}+5a^{3}-27a^{2}+6a+12$ |
| 13.1-a2 |
13.1-a |
$2$ |
$7$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{7} \) |
$117.85504$ |
$(a^3-a^2-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.732786306$ |
1.65192 |
\( -\frac{89657653277597438860400}{62748517} a^{5} + \frac{211537721487214382113224}{62748517} a^{4} + \frac{295663198706217104707728}{62748517} a^{3} - \frac{654814741650010696365434}{62748517} a^{2} - \frac{182765819832947911536958}{62748517} a + \frac{338028864861763693702861}{62748517} \) |
\( \bigl[a^{2} - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 3\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 3 a + 2\) , \( -11 a^{5} + 22 a^{4} + 109 a^{3} - 81 a^{2} - 373 a - 217\) , \( -205 a^{5} + 433 a^{4} + 1350 a^{3} - 1410 a^{2} - 3578 a - 1520\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+3\right){x}^{2}+\left(-11a^{5}+22a^{4}+109a^{3}-81a^{2}-373a-217\right){x}-205a^{5}+433a^{4}+1350a^{3}-1410a^{2}-3578a-1520$ |
| 13.1-b1 |
13.1-b |
$2$ |
$7$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$117.85504$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$0.010100240$ |
$45897.50687$ |
2.61151 |
\( \frac{124200}{13} a^{5} - \frac{154732}{13} a^{4} - \frac{604704}{13} a^{3} + \frac{256238}{13} a^{2} + \frac{701798}{13} a + \frac{201965}{13} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{4} - 2 a^{2} + 1\) , \( a^{3} + a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(a^{4}-2a^{2}+1\right){x}+a^{3}+a^{2}-a-1$ |
| 13.1-b2 |
13.1-b |
$2$ |
$7$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{7} \) |
$117.85504$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 7 \) |
$0.070701683$ |
$936.6838138$ |
2.61151 |
\( -\frac{89657653277597438860400}{62748517} a^{5} + \frac{211537721487214382113224}{62748517} a^{4} + \frac{295663198706217104707728}{62748517} a^{3} - \frac{654814741650010696365434}{62748517} a^{2} - \frac{182765819832947911536958}{62748517} a + \frac{338028864861763693702861}{62748517} \) |
\( \bigl[-a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 3 a + 2\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 8 a^{2} + 7 a - 4\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + a + 4\) , \( 2842 a^{5} - 7060 a^{4} - 8630 a^{3} + 22227 a^{2} + 3810 a - 12805\) , \( -159047 a^{5} + 350935 a^{4} + 552971 a^{3} - 1052739 a^{2} - 368298 a + 515171\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+3a+2\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+a+4\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-9a^{3}+8a^{2}+7a-4\right){x}^{2}+\left(2842a^{5}-7060a^{4}-8630a^{3}+22227a^{2}+3810a-12805\right){x}-159047a^{5}+350935a^{4}+552971a^{3}-1052739a^{2}-368298a+515171$ |
| 19.1-a1 |
19.1-a |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
|
\( 2^{2} \) |
$1$ |
$4780.662197$ |
3.00246 |
\( \frac{1739160042131728}{130321} a^{5} - \frac{4932952290531667}{130321} a^{4} - \frac{149053831288821}{6859} a^{3} + \frac{12803090229732071}{130321} a^{2} - \frac{3745685345957208}{130321} a - \frac{2077579561866287}{130321} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 36 a^{5} - 86 a^{4} - 112 a^{3} + 256 a^{2} + 62 a - 133\) , \( 8 a^{5} - 13 a^{4} - 45 a^{3} + 62 a^{2} + 32 a - 33\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+1\right){x}^{2}+\left(36a^{5}-86a^{4}-112a^{3}+256a^{2}+62a-133\right){x}+8a^{5}-13a^{4}-45a^{3}+62a^{2}+32a-33$ |
| 19.1-a2 |
19.1-a |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
|
\( 2 \) |
$1$ |
$4780.662197$ |
3.00246 |
\( -\frac{18123410}{361} a^{5} + \frac{52965955}{361} a^{4} + \frac{1405313}{19} a^{3} - \frac{138485321}{361} a^{2} + \frac{44309085}{361} a + \frac{24067076}{361} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -9 a^{5} + 19 a^{4} + 33 a^{3} - 59 a^{2} - 23 a + 32\) , \( -9 a^{5} + 20 a^{4} + 31 a^{3} - 61 a^{2} - 20 a + 32\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+1\right){x}^{2}+\left(-9a^{5}+19a^{4}+33a^{3}-59a^{2}-23a+32\right){x}-9a^{5}+20a^{4}+31a^{3}-61a^{2}-20a+32$ |
| 19.1-a3 |
19.1-a |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{20} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
|
\( 2^{2} \cdot 5 \) |
$1$ |
$191.2264878$ |
3.00246 |
\( -\frac{1173942650596473834829166750874259366994}{37589973457545958193355601} a^{5} + \frac{2676187016923375604981703243580200746439}{37589973457545958193355601} a^{4} + \frac{207755452393643183233675622498278998760}{1978419655660313589123979} a^{3} - \frac{8147549816623980843393405138452057696674}{37589973457545958193355601} a^{2} - \frac{2417261516356057079989627455703362986660}{37589973457545958193355601} a + \frac{4197823669693440279467208875908040893922}{37589973457545958193355601} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 3\) , \( a^{2} - 1\) , \( 163 a^{5} - 752 a^{4} + 584 a^{3} + 1131 a^{2} - 776 a - 784\) , \( 2687 a^{5} - 14457 a^{4} + 19343 a^{3} + 7827 a^{2} - 18906 a - 1445\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+3\right){x}^{2}+\left(163a^{5}-752a^{4}+584a^{3}+1131a^{2}-776a-784\right){x}+2687a^{5}-14457a^{4}+19343a^{3}+7827a^{2}-18906a-1445$ |
| 19.1-a4 |
19.1-a |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{10} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
|
\( 2 \cdot 5 \) |
$1$ |
$191.2264878$ |
3.00246 |
\( -\frac{433221147565945895303229498426}{6131066257801} a^{5} + \frac{1544972731160740998611309370232}{6131066257801} a^{4} - \frac{36153742951077897649211802299}{322687697779} a^{3} - \frac{1523440257471812573192296926321}{6131066257801} a^{2} + \frac{653196004835181155701191143566}{6131066257801} a + \frac{276598610974242425825826341352}{6131066257801} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2}\) , \( 3 a^{5} - 62 a^{4} - 12 a^{3} + 182 a^{2} - 6 a - 81\) , \( 149 a^{5} + 231 a^{4} - 255 a^{3} - 473 a^{2} + 19 a + 240\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){x}{y}+\left(-a^{5}+2a^{4}+3a^{3}-4a^{2}\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a\right){x}^{2}+\left(3a^{5}-62a^{4}-12a^{3}+182a^{2}-6a-81\right){x}+149a^{5}+231a^{4}-255a^{3}-473a^{2}+19a+240$ |
| 19.1-b1 |
19.1-b |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$83544.44148$ |
1.56880 |
\( \frac{1739160042131728}{130321} a^{5} - \frac{4932952290531667}{130321} a^{4} - \frac{149053831288821}{6859} a^{3} + \frac{12803090229732071}{130321} a^{2} - \frac{3745685345957208}{130321} a - \frac{2077579561866287}{130321} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 9 a^{2} + a - 3\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 3 a + 2\) , \( -a^{5} + a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( -6 a^{5} + 8 a^{4} + 32 a^{3} - 2 a^{2} - 15 a - 3\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+3a+2\right){y}={x}^{3}+\left(2a^{5}-4a^{4}-6a^{3}+9a^{2}+a-3\right){x}^{2}+\left(-a^{5}+a^{4}-a^{3}-5a^{2}+4a+2\right){x}-6a^{5}+8a^{4}+32a^{3}-2a^{2}-15a-3$ |
| 19.1-b2 |
19.1-b |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$83544.44148$ |
1.56880 |
\( -\frac{18123410}{361} a^{5} + \frac{52965955}{361} a^{4} + \frac{1405313}{19} a^{3} - \frac{138485321}{361} a^{2} + \frac{44309085}{361} a + \frac{24067076}{361} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 9 a^{2} + a - 3\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 3 a + 2\) , \( -a^{5} + a^{4} + 4 a^{3} - a + 2\) , \( a^{5} - 4 a^{3} - 2 a^{2} + 3 a\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+3a+2\right){y}={x}^{3}+\left(2a^{5}-4a^{4}-6a^{3}+9a^{2}+a-3\right){x}^{2}+\left(-a^{5}+a^{4}+4a^{3}-a+2\right){x}+a^{5}-4a^{3}-2a^{2}+3a$ |
| 19.1-b3 |
19.1-b |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{20} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$5.346844254$ |
1.56880 |
\( -\frac{1173942650596473834829166750874259366994}{37589973457545958193355601} a^{5} + \frac{2676187016923375604981703243580200746439}{37589973457545958193355601} a^{4} + \frac{207755452393643183233675622498278998760}{1978419655660313589123979} a^{3} - \frac{8147549816623980843393405138452057696674}{37589973457545958193355601} a^{2} - \frac{2417261516356057079989627455703362986660}{37589973457545958193355601} a + \frac{4197823669693440279467208875908040893922}{37589973457545958193355601} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -140 a^{5} + 458 a^{4} + 165 a^{3} - 1343 a^{2} + 335 a + 197\) , \( -862 a^{5} + 3252 a^{4} + 319 a^{3} - 9896 a^{2} + 3257 a + 1670\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-140a^{5}+458a^{4}+165a^{3}-1343a^{2}+335a+197\right){x}-862a^{5}+3252a^{4}+319a^{3}-9896a^{2}+3257a+1670$ |
| 19.1-b4 |
19.1-b |
$4$ |
$10$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{10} \) |
$121.64167$ |
$(a^4-a^3-5a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$5.346844254$ |
1.56880 |
\( -\frac{433221147565945895303229498426}{6131066257801} a^{5} + \frac{1544972731160740998611309370232}{6131066257801} a^{4} - \frac{36153742951077897649211802299}{322687697779} a^{3} - \frac{1523440257471812573192296926321}{6131066257801} a^{2} + \frac{653196004835181155701191143566}{6131066257801} a + \frac{276598610974242425825826341352}{6131066257801} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 4\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( 1748 a^{5} - 3995 a^{4} - 5860 a^{3} + 12168 a^{2} + 3565 a - 6290\) , \( 55688 a^{5} - 126978 a^{4} - 187202 a^{3} + 386601 a^{2} + 114573 a - 199250\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+4\right){x}^{2}+\left(1748a^{5}-3995a^{4}-5860a^{3}+12168a^{2}+3565a-6290\right){x}+55688a^{5}-126978a^{4}-187202a^{3}+386601a^{2}+114573a-199250$ |
| 23.1-a1 |
23.1-a |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{8} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$62.78587596$ |
1.88639 |
\( \frac{603906513465985582083371347330}{78310985281} a^{5} - \frac{1712946601215233048210947595849}{78310985281} a^{4} - \frac{982843297041006866606418212734}{78310985281} a^{3} + \frac{4445531799661962039643555992986}{78310985281} a^{2} - \frac{1302809362010490409255778164171}{78310985281} a - \frac{721993341117769982805626867557}{78310985281} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 3\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + a + 3\) , \( 13 a^{5} - 26 a^{4} - 59 a^{3} + 76 a^{2} + 46 a - 49\) , \( -30 a^{5} + 65 a^{4} + 63 a^{3} - 250 a^{2} - 22 a + 118\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+a+3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-3a+3\right){x}^{2}+\left(13a^{5}-26a^{4}-59a^{3}+76a^{2}+46a-49\right){x}-30a^{5}+65a^{4}+63a^{3}-250a^{2}-22a+118$ |
| 23.1-a2 |
23.1-a |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{4} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$4018.296061$ |
1.88639 |
\( \frac{262102157557760}{279841} a^{5} - \frac{785863592463542}{279841} a^{4} - \frac{283474548932665}{279841} a^{3} + \frac{1935796803513840}{279841} a^{2} - \frac{914381614853616}{279841} a - \frac{70465860813659}{279841} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 3\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + a + 3\) , \( 13 a^{5} - 31 a^{4} - 44 a^{3} + 96 a^{2} + 31 a - 54\) , \( -32 a^{5} + 74 a^{4} + 104 a^{3} - 225 a^{2} - 57 a + 110\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+a+3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-3a+3\right){x}^{2}+\left(13a^{5}-31a^{4}-44a^{3}+96a^{2}+31a-54\right){x}-32a^{5}+74a^{4}+104a^{3}-225a^{2}-57a+110$ |
| 23.1-a3 |
23.1-a |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16073.18424$ |
1.88639 |
\( -\frac{2325302}{529} a^{5} + \frac{11664192}{529} a^{4} - \frac{10145924}{529} a^{3} - \frac{24581540}{529} a^{2} + \frac{36199583}{529} a - \frac{6234222}{529} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 4 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - 2 a - 2\) , \( 0\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 13 a^{2} - 1\) , \( 0\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-4a\right){x}{y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}-2a-2\right){x}^{2}+\left(2a^{5}-5a^{4}-5a^{3}+13a^{2}-1\right){x}$ |
| 23.1-a4 |
23.1-a |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1004.574015$ |
1.88639 |
\( -\frac{215428349561756857634}{529} a^{5} + \frac{492514390836274565273}{529} a^{4} + \frac{722223691292383809502}{529} a^{3} - \frac{1501520438226610059450}{529} a^{2} - \frac{438612747377786951749}{529} a + \frac{777010070074074406725}{529} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 4 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - 2 a - 2\) , \( 0\) , \( -53 a^{5} + 65 a^{4} + 275 a^{3} - 147 a^{2} - 305 a - 76\) , \( -448 a^{5} + 551 a^{4} + 2266 a^{3} - 1156 a^{2} - 2449 a - 539\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-4a\right){x}{y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}-2a-2\right){x}^{2}+\left(-53a^{5}+65a^{4}+275a^{3}-147a^{2}-305a-76\right){x}-448a^{5}+551a^{4}+2266a^{3}-1156a^{2}-2449a-539$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$6092.566841$ |
1.43008 |
\( \frac{2863830352}{12167} a^{5} - \frac{8110145855}{12167} a^{4} - \frac{4767593785}{12167} a^{3} + \frac{20999959650}{12167} a^{2} - \frac{5269424726}{12167} a - \frac{4022677559}{12167} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 4 a - 3\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 10 a^{2} - 4 a + 2\) , \( -2 a^{5} + 2 a^{4} + 8 a^{3} - 2 a^{2} - a + 1\) , \( -9 a^{5} + 11 a^{4} + 43 a^{3} - 18 a^{2} - 46 a - 12\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+\left(-2a^{5}+4a^{4}+7a^{3}-10a^{2}-4a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+4a-3\right){x}^{2}+\left(-2a^{5}+2a^{4}+8a^{3}-2a^{2}-a+1\right){x}-9a^{5}+11a^{4}+43a^{3}-18a^{2}-46a-12$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{6} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$3046.283420$ |
1.43008 |
\( -\frac{325262592875422920}{148035889} a^{5} + \frac{888287579292784957}{148035889} a^{4} + \frac{529168207682933874}{148035889} a^{3} - \frac{1866860822611790771}{148035889} a^{2} - \frac{262809050143853797}{148035889} a + \frac{827990804170004077}{148035889} \) |
\( \bigl[-2 a^{5} + 4 a^{4} + 7 a^{3} - 10 a^{2} - 3 a + 2\) , \( -a^{5} + a^{4} + 5 a^{3} - a^{2} - 6 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( 28 a^{5} - 14 a^{4} - 131 a^{3} - 35 a^{2} + 53 a + 12\) , \( -116 a^{5} + 64 a^{4} + 555 a^{3} + 107 a^{2} - 303 a - 83\bigr] \) |
${y}^2+\left(-2a^{5}+4a^{4}+7a^{3}-10a^{2}-3a+2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-a^{2}-6a-2\right){x}^{2}+\left(28a^{5}-14a^{4}-131a^{3}-35a^{2}+53a+12\right){x}-116a^{5}+64a^{4}+555a^{3}+107a^{2}-303a-83$ |
| 23.1-c1 |
23.1-c |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.021206091$ |
$85125.61280$ |
2.54232 |
\( -\frac{65640755}{23} a^{5} + \frac{40838980}{23} a^{4} + \frac{326084770}{23} a^{3} + \frac{67333372}{23} a^{2} - \frac{172368644}{23} a - \frac{46704520}{23} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 18 a^{2} - a - 4\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 3\) , \( -13 a^{5} + 36 a^{4} + 22 a^{3} - 94 a^{2} + 25 a + 17\) , \( -172 a^{5} + 486 a^{4} + 283 a^{3} - 1258 a^{2} + 367 a + 203\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+3\right){y}={x}^{3}+\left(3a^{5}-7a^{4}-8a^{3}+18a^{2}-a-4\right){x}^{2}+\left(-13a^{5}+36a^{4}+22a^{3}-94a^{2}+25a+17\right){x}-172a^{5}+486a^{4}+283a^{3}-1258a^{2}+367a+203$ |
| 23.1-c2 |
23.1-c |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.042412183$ |
$21281.40320$ |
2.54232 |
\( \frac{2345699603787355}{529} a^{5} + \frac{1074875692843158}{529} a^{4} - \frac{6739674666621324}{529} a^{3} - \frac{2493758564659293}{529} a^{2} + \frac{3250456472311806}{529} a + \frac{954069874300768}{529} \) |
\( \bigl[-a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 3 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 3 a + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 1\) , \( 19 a^{5} - 59 a^{4} - a^{3} + 82 a^{2} - 7 a - 26\) , \( 60 a^{5} - 221 a^{4} + 123 a^{3} + 198 a^{2} - 111 a - 26\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+3a+1\right){x}{y}+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-3a+3\right){x}^{2}+\left(19a^{5}-59a^{4}-a^{3}+82a^{2}-7a-26\right){x}+60a^{5}-221a^{4}+123a^{3}+198a^{2}-111a-26$ |
| 23.1-d1 |
23.1-d |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9168.445561$ |
2.15206 |
\( -\frac{65640755}{23} a^{5} + \frac{40838980}{23} a^{4} + \frac{326084770}{23} a^{3} + \frac{67333372}{23} a^{2} - \frac{172368644}{23} a - \frac{46704520}{23} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 10 a^{2} + 4 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 1\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 8 a^{2} + 6 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}-1\right){y}={x}^{3}+\left(2a^{5}-4a^{4}-7a^{3}+10a^{2}+4a-1\right){x}^{2}+\left(2a^{5}-3a^{4}-9a^{3}+8a^{2}+6a\right){x}+a^{4}-2a^{3}-3a^{2}+4a+1$ |
| 23.1-d2 |
23.1-d |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4584.222780$ |
2.15206 |
\( \frac{2345699603787355}{529} a^{5} + \frac{1074875692843158}{529} a^{4} - \frac{6739674666621324}{529} a^{3} - \frac{2493758564659293}{529} a^{2} + \frac{3250456472311806}{529} a + \frac{954069874300768}{529} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 2 a - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 287 a^{5} - 656 a^{4} - 963 a^{3} + 1990 a^{2} + 593 a - 1024\) , \( 3252 a^{5} - 7420 a^{4} - 10920 a^{3} + 22569 a^{2} + 6684 a - 11625\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+2a-3\right){x}^{2}+\left(287a^{5}-656a^{4}-963a^{3}+1990a^{2}+593a-1024\right){x}+3252a^{5}-7420a^{4}-10920a^{3}+22569a^{2}+6684a-11625$ |
| 23.1-e1 |
23.1-e |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.008416507$ |
$88546.81633$ |
3.14874 |
\( \frac{2863830352}{12167} a^{5} - \frac{8110145855}{12167} a^{4} - \frac{4767593785}{12167} a^{3} + \frac{20999959650}{12167} a^{2} - \frac{5269424726}{12167} a - \frac{4022677559}{12167} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + a + 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} - 2 a\) , \( -3 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 3\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+a+2\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a\right){x}^{2}+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}-2a\right){x}-3a^{4}+4a^{3}+9a^{2}-9a-3$ |
| 23.1-e2 |
23.1-e |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{6} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.016833014$ |
$22136.70408$ |
3.14874 |
\( -\frac{325262592875422920}{148035889} a^{5} + \frac{888287579292784957}{148035889} a^{4} + \frac{529168207682933874}{148035889} a^{3} - \frac{1866860822611790771}{148035889} a^{2} - \frac{262809050143853797}{148035889} a + \frac{827990804170004077}{148035889} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -2 a^{5} + 4 a^{4} + 6 a^{3} - 9 a^{2} + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( -3 a^{5} - 18 a^{4} + 43 a^{3} + 95 a^{2} - 73 a - 99\) , \( -131 a^{5} + 215 a^{4} + 565 a^{3} - 533 a^{2} - 549 a + 89\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+6a^{3}-9a^{2}+3\right){x}^{2}+\left(-3a^{5}-18a^{4}+43a^{3}+95a^{2}-73a-99\right){x}-131a^{5}+215a^{4}+565a^{3}-533a^{2}-549a+89$ |
| 23.1-f1 |
23.1-f |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{8} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.172747682$ |
$1310.995111$ |
2.55161 |
\( \frac{603906513465985582083371347330}{78310985281} a^{5} - \frac{1712946601215233048210947595849}{78310985281} a^{4} - \frac{982843297041006866606418212734}{78310985281} a^{3} + \frac{4445531799661962039643555992986}{78310985281} a^{2} - \frac{1302809362010490409255778164171}{78310985281} a - \frac{721993341117769982805626867557}{78310985281} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 2\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 2\) , \( 1564 a^{5} - 3548 a^{4} - 5328 a^{3} + 10909 a^{2} + 3267 a - 5643\) , \( 46178 a^{5} - 105484 a^{4} - 154457 a^{3} + 319944 a^{2} + 94490 a - 164658\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){x}^{2}+\left(1564a^{5}-3548a^{4}-5328a^{3}+10909a^{2}+3267a-5643\right){x}+46178a^{5}-105484a^{4}-154457a^{3}+319944a^{2}+94490a-164658$ |
| 23.1-f2 |
23.1-f |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{4} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.345495365$ |
$5243.980447$ |
2.55161 |
\( \frac{262102157557760}{279841} a^{5} - \frac{785863592463542}{279841} a^{4} - \frac{283474548932665}{279841} a^{3} + \frac{1935796803513840}{279841} a^{2} - \frac{914381614853616}{279841} a - \frac{70465860813659}{279841} \) |
\( \bigl[-a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - a\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 3\) , \( -16 a^{5} - 11 a^{4} + 28 a^{3} + 7 a^{2} - 8 a\) , \( -155 a^{5} - 57 a^{4} + 477 a^{3} + 171 a^{2} - 234 a - 71\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+3a^{3}-4a^{2}-a\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){x}^{2}+\left(-16a^{5}-11a^{4}+28a^{3}+7a^{2}-8a\right){x}-155a^{5}-57a^{4}+477a^{3}+171a^{2}-234a-71$ |
| 23.1-f3 |
23.1-f |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.172747682$ |
$20975.92178$ |
2.55161 |
\( -\frac{2325302}{529} a^{5} + \frac{11664192}{529} a^{4} - \frac{10145924}{529} a^{3} - \frac{24581540}{529} a^{2} + \frac{36199583}{529} a - \frac{6234222}{529} \) |
\( \bigl[-2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a - 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 2\) , \( -5 a^{5} + 14 a^{4} + 7 a^{3} - 35 a^{2} + 15 a + 6\) , \( a^{5} - 5 a^{4} + a^{3} + 15 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+3\right){x}{y}+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a-1\right){x}^{2}+\left(-5a^{5}+14a^{4}+7a^{3}-35a^{2}+15a+6\right){x}+a^{5}-5a^{4}+a^{3}+15a^{2}-5a-3$ |
| 23.1-f4 |
23.1-f |
$4$ |
$4$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$123.59385$ |
$(2a^5-4a^4-7a^3+10a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$0.690990730$ |
$81.93719448$ |
2.55161 |
\( -\frac{215428349561756857634}{529} a^{5} + \frac{492514390836274565273}{529} a^{4} + \frac{722223691292383809502}{529} a^{3} - \frac{1501520438226610059450}{529} a^{2} - \frac{438612747377786951749}{529} a + \frac{777010070074074406725}{529} \) |
\( \bigl[-2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a - 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 2\) , \( -130 a^{5} + 359 a^{4} + 257 a^{3} - 940 a^{2} + 120 a + 96\) , \( 710 a^{5} - 2128 a^{4} - 769 a^{3} + 5499 a^{2} - 2720 a - 1208\bigr] \) |
${y}^2+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+3\right){x}{y}+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a-1\right){x}^{2}+\left(-130a^{5}+359a^{4}+257a^{3}-940a^{2}+120a+96\right){x}+710a^{5}-2128a^{4}-769a^{3}+5499a^{2}-2720a-1208$ |
| 49.1-a1 |
49.1-a |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$131.63435$ |
$(-a^5+a^4+5a^3-a^2-5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.005223776$ |
$60056.56655$ |
3.53464 |
\( -7521 a^{5} + 9447 a^{4} + 37710 a^{3} - 19629 a^{2} - 42407 a - 7286 \) |
\( \bigl[a + 1\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 7 a^{2} + 9 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 4 a^{2} + 9 a + 6\) , \( 3 a^{5} - 7 a^{4} - 9 a^{3} + 18 a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a+1\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-9a^{3}+7a^{2}+9a-2\right){x}^{2}+\left(2a^{5}-3a^{4}-9a^{3}+4a^{2}+9a+6\right){x}+3a^{5}-7a^{4}-9a^{3}+18a^{2}+3a-3$ |
| 49.1-b1 |
49.1-b |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$131.63435$ |
$(-a^5+a^4+5a^3-a^2-5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.018289270$ |
$35882.36064$ |
3.69699 |
\( -20282 a^{5} + 23909 a^{4} + 102706 a^{3} - 42330 a^{2} - 121294 a - 26598 \) |
\( \bigl[-2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - 2 a\) , \( -a^{2} + a\bigr] \) |
${y}^2+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+4\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+3a-1\right){x}^{2}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-2a\right){x}-a^{2}+a$ |
| 49.1-c1 |
49.1-c |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{13} \) |
$131.63435$ |
$(-a^5+a^4+5a^3-a^2-5a-3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
|
\( 2 \) |
$1$ |
$829.4575927$ |
3.71642 |
\( -\frac{608369349585}{823543} a^{5} + \frac{202587485997}{117649} a^{4} + \frac{1948072798037}{823543} a^{3} - \frac{4245581101481}{823543} a^{2} - \frac{145027930896}{117649} a + \frac{2041081689113}{823543} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 4 a - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( -4 a^{5} + 12 a^{4} + 5 a^{3} - 31 a^{2} + 13 a + 4\) , \( -12 a^{5} + 29 a^{4} + 30 a^{3} - 72 a^{2} + a + 6\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+4a-3\right){x}^{2}+\left(-4a^{5}+12a^{4}+5a^{3}-31a^{2}+13a+4\right){x}-12a^{5}+29a^{4}+30a^{3}-72a^{2}+a+6$ |
| 49.1-d1 |
49.1-d |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{13} \) |
$131.63435$ |
$(-a^5+a^4+5a^3-a^2-5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.017500812$ |
$8431.429405$ |
3.32499 |
\( -\frac{608369349585}{823543} a^{5} + \frac{202587485997}{117649} a^{4} + \frac{1948072798037}{823543} a^{3} - \frac{4245581101481}{823543} a^{2} - \frac{145027930896}{117649} a + \frac{2041081689113}{823543} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 7 a^{2} - 9 a + 2\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 4\) , \( -3 a^{5} + 8 a^{4} + 8 a^{3} - 26 a^{2} + 5 a + 11\) , \( -3 a^{5} + 8 a^{4} + 5 a^{3} - 14 a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+4\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+9a^{3}-7a^{2}-9a+2\right){x}^{2}+\left(-3a^{5}+8a^{4}+8a^{3}-26a^{2}+5a+11\right){x}-3a^{5}+8a^{4}+5a^{3}-14a^{2}-2a+1$ |
| 49.1-e1 |
49.1-e |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$131.63435$ |
$(-a^5+a^4+5a^3-a^2-5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.005332193$ |
$126429.5721$ |
3.79774 |
\( -20282 a^{5} + 23909 a^{4} + 102706 a^{3} - 42330 a^{2} - 121294 a - 26598 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{4} + a^{3} + 4 a^{2}\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( -2 a^{5} - 2 a^{4} + 15 a^{3} + 7 a^{2} - 6 a\) , \( -16 a^{5} + 46 a^{4} - 3 a^{3} - 39 a^{2} + 10 a + 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+5a-1\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}\right){x}^{2}+\left(-2a^{5}-2a^{4}+15a^{3}+7a^{2}-6a\right){x}-16a^{5}+46a^{4}-3a^{3}-39a^{2}+10a+5$ |
| 49.1-f1 |
49.1-f |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$131.63435$ |
$(-a^5+a^4+5a^3-a^2-5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.007991537$ |
$40922.37853$ |
3.68461 |
\( -7521 a^{5} + 9447 a^{4} + 37710 a^{3} - 19629 a^{2} - 42407 a - 7286 \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 3 a^{2} - 3 a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( 2 a^{5} - 8 a^{4} + 22 a^{2} - 8 a - 2\) , \( 2 a^{5} - 6 a^{4} - 3 a^{3} + 16 a^{2} - 4 a - 3\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-2a^{3}+3a^{2}-3a+1\right){x}^{2}+\left(2a^{5}-8a^{4}+22a^{2}-8a-2\right){x}+2a^{5}-6a^{4}-3a^{3}+16a^{2}-4a-3$ |
| 67.1-a1 |
67.1-a |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
67.1 |
\( 67 \) |
\( 67 \) |
$135.11154$ |
$(-a^5+a^4+5a^3-a^2-5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1.250243972$ |
$609.9423781$ |
4.29590 |
\( -\frac{2573917486267}{67} a^{5} + \frac{3343947332410}{67} a^{4} + \frac{16112434016460}{67} a^{3} + \frac{2527790959352}{67} a^{2} - \frac{8699696377803}{67} a - \frac{2303055246971}{67} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 4 a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 14 a^{2} - a - 5\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 4 a\) , \( -15 a^{5} + 45 a^{4} + 27 a^{3} - 133 a^{2} + 29 a + 22\) , \( -91 a^{5} + 267 a^{4} + 148 a^{3} - 737 a^{2} + 219 a + 119\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+4a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+4a\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-5a^{3}+14a^{2}-a-5\right){x}^{2}+\left(-15a^{5}+45a^{4}+27a^{3}-133a^{2}+29a+22\right){x}-91a^{5}+267a^{4}+148a^{3}-737a^{2}+219a+119$ |
| 67.1-a2 |
67.1-a |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
67.1 |
\( 67 \) |
\( 67^{2} \) |
$135.11154$ |
$(-a^5+a^4+5a^3-a^2-5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.625121986$ |
$2439.769512$ |
4.29590 |
\( \frac{298672405}{4489} a^{5} - \frac{245024637}{4489} a^{4} - \frac{1639659706}{4489} a^{3} - \frac{336980917}{4489} a^{2} + \frac{906699670}{4489} a + \frac{246011751}{4489} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} - a - 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 6 a^{2} - a + 2\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+3a-1\right){x}^{2}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}-a-1\right){x}-a^{5}+2a^{4}+3a^{3}-6a^{2}-a+2$ |
| 67.1-b1 |
67.1-b |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
67.1 |
\( 67 \) |
\( 67 \) |
$135.11154$ |
$(-a^5+a^4+5a^3-a^2-5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.037179509$ |
$18021.97383$ |
3.77465 |
\( -\frac{2573917486267}{67} a^{5} + \frac{3343947332410}{67} a^{4} + \frac{16112434016460}{67} a^{3} + \frac{2527790959352}{67} a^{2} - \frac{8699696377803}{67} a - \frac{2303055246971}{67} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{3} - a^{2} - 3 a\) , \( -48 a^{5} + 126 a^{4} + 95 a^{3} - 319 a^{2} + 63 a + 35\) , \( 194 a^{5} - 563 a^{4} - 285 a^{3} + 1476 a^{2} - 490 a - 272\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+1\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2\right){x}^{2}+\left(-48a^{5}+126a^{4}+95a^{3}-319a^{2}+63a+35\right){x}+194a^{5}-563a^{4}-285a^{3}+1476a^{2}-490a-272$ |
| 67.1-b2 |
67.1-b |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
67.1 |
\( 67 \) |
\( 67^{2} \) |
$135.11154$ |
$(-a^5+a^4+5a^3-a^2-5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.018589754$ |
$72087.89535$ |
3.77465 |
\( \frac{298672405}{4489} a^{5} - \frac{245024637}{4489} a^{4} - \frac{1639659706}{4489} a^{3} - \frac{336980917}{4489} a^{2} + \frac{906699670}{4489} a + \frac{246011751}{4489} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 5 a^{2} + 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( 2 a^{5} - 3 a^{4} - 7 a^{3} + 4 a^{2} + 4 a - 1\) , \( 3 a^{5} - 7 a^{4} - 10 a^{3} + 21 a^{2} + 8 a - 12\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-5a^{2}+2\right){x}^{2}+\left(2a^{5}-3a^{4}-7a^{3}+4a^{2}+4a-1\right){x}+3a^{5}-7a^{4}-10a^{3}+21a^{2}+8a-12$ |
| 79.1-a1 |
79.1-a |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$136.97936$ |
$(a^3-a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2903.096668$ |
2.72572 |
\( -\frac{1520034}{79} a^{5} + \frac{59346}{79} a^{4} + \frac{4147477}{79} a^{3} - \frac{354978}{79} a^{2} - \frac{1449513}{79} a - \frac{147653}{79} \) |
\( \bigl[a^{2} - 1\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 15 a^{2} + 5 a - 3\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + a + 4\) , \( 14 a^{5} - 31 a^{4} - 47 a^{3} + 92 a^{2} + 27 a - 41\) , \( -7 a^{5} + 21 a^{4} + 9 a^{3} - 46 a^{2} - a + 20\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+a+4\right){y}={x}^{3}+\left(3a^{5}-6a^{4}-10a^{3}+15a^{2}+5a-3\right){x}^{2}+\left(14a^{5}-31a^{4}-47a^{3}+92a^{2}+27a-41\right){x}-7a^{5}+21a^{4}+9a^{3}-46a^{2}-a+20$ |
| 79.1-b1 |
79.1-b |
$1$ |
$1$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$136.97936$ |
$(a^3-a^2-4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.008335847$ |
$69454.95486$ |
3.26154 |
\( -\frac{1520034}{79} a^{5} + \frac{59346}{79} a^{4} + \frac{4147477}{79} a^{3} - \frac{354978}{79} a^{2} - \frac{1449513}{79} a - \frac{147653}{79} \) |
\( \bigl[-a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 2 a\) , \( 4 a^{5} - 12 a^{4} - 7 a^{3} + 33 a^{2} - 7 a - 5\) , \( 3 a^{5} - 9 a^{4} - 4 a^{3} + 23 a^{2} - 8 a - 4\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+4a+2\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a-2\right){x}^{2}+\left(4a^{5}-12a^{4}-7a^{3}+33a^{2}-7a-5\right){x}+3a^{5}-9a^{4}-4a^{3}+23a^{2}-8a-4$ |
| 79.2-a1 |
79.2-a |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1282.484086$ |
2.40825 |
\( -\frac{1940595618432930397244}{6241} a^{5} + \frac{1033731254451145901538}{6241} a^{4} + \frac{9279189144648286228459}{6241} a^{3} + \frac{1971895430972964623557}{6241} a^{2} - \frac{4868995888688881239841}{6241} a - \frac{1322551107817623492543}{6241} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 3 a - 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} + 3\) , \( 1301 a^{5} - 2973 a^{4} - 4363 a^{3} + 9046 a^{2} + 2671 a - 4660\) , \( 37234 a^{5} - 84879 a^{4} - 125208 a^{3} + 258435 a^{2} + 76676 a - 133156\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}-2\right){x}{y}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-3a-1\right){x}^{2}+\left(1301a^{5}-2973a^{4}-4363a^{3}+9046a^{2}+2671a-4660\right){x}+37234a^{5}-84879a^{4}-125208a^{3}+258435a^{2}+76676a-133156$ |
| 79.2-a2 |
79.2-a |
$2$ |
$2$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$10259.87269$ |
2.40825 |
\( -\frac{17321735556}{79} a^{5} + \frac{13228915757}{79} a^{4} + \frac{79605577118}{79} a^{3} - \frac{675602135}{79} a^{2} - \frac{42526871857}{79} a - \frac{1963530046}{79} \) |
\( \bigl[-2 a^{5} + 4 a^{4} + 7 a^{3} - 10 a^{2} - 4 a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 3\) , \( 1\) , \( 4 a^{5} - 9 a^{4} - 14 a^{3} + 26 a^{2} + 9 a - 12\) , \( -4 a^{5} + 2 a^{4} + 25 a^{3} + 5 a^{2} - 35 a - 21\bigr] \) |
${y}^2+\left(-2a^{5}+4a^{4}+7a^{3}-10a^{2}-4a+3\right){x}{y}+{y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a-3\right){x}^{2}+\left(4a^{5}-9a^{4}-14a^{3}+26a^{2}+9a-12\right){x}-4a^{5}+2a^{4}+25a^{3}+5a^{2}-35a-21$ |
| 79.2-b1 |
79.2-b |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$5.607042530$ |
$15.44189466$ |
3.90207 |
\( -\frac{23056887399498782353187}{6241} a^{5} + \frac{12282118445872874540738}{6241} a^{4} + \frac{110249254127088991226931}{6241} a^{3} + \frac{23428771302249586031484}{6241} a^{2} - \frac{57850223421360506122838}{6241} a - \frac{15713686931776062246680}{6241} \) |
\( \bigl[-2 a^{5} + 4 a^{4} + 7 a^{3} - 10 a^{2} - 4 a + 3\) , \( -3 a^{5} + 5 a^{4} + 12 a^{3} - 12 a^{2} - 9 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 3\) , \( 43 a^{5} - 135 a^{4} + 3 a^{3} + 172 a^{2} - 5 a - 45\) , \( 454 a^{5} - 1578 a^{4} + 532 a^{3} + 1782 a^{2} - 591 a - 476\bigr] \) |
${y}^2+\left(-2a^{5}+4a^{4}+7a^{3}-10a^{2}-4a+3\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+3\right){y}={x}^{3}+\left(-3a^{5}+5a^{4}+12a^{3}-12a^{2}-9a+3\right){x}^{2}+\left(43a^{5}-135a^{4}+3a^{3}+172a^{2}-5a-45\right){x}+454a^{5}-1578a^{4}+532a^{3}+1782a^{2}-591a-476$ |
| 79.2-b2 |
79.2-b |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{4} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.803521265$ |
$988.2812586$ |
3.90207 |
\( -\frac{25578474509197103}{38950081} a^{5} + \frac{13769208943393063}{38950081} a^{4} + \frac{122006081712216622}{38950081} a^{3} + \frac{25777818166571072}{38950081} a^{2} - \frac{63987895436719587}{38950081} a - \frac{17369745196758095}{38950081} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 18 a^{2} - a - 5\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 2\) , \( -4 a^{5} + 15 a^{4} - 42 a^{2} + 18 a + 3\) , \( -90 a^{5} + 257 a^{4} + 143 a^{3} - 671 a^{2} + 197 a + 108\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+a+2\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+4a+2\right){y}={x}^{3}+\left(3a^{5}-7a^{4}-8a^{3}+18a^{2}-a-5\right){x}^{2}+\left(-4a^{5}+15a^{4}-42a^{2}+18a+3\right){x}-90a^{5}+257a^{4}+143a^{3}-671a^{2}+197a+108$ |
| 79.2-b3 |
79.2-b |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.401760632$ |
$3953.125034$ |
3.90207 |
\( \frac{60329185}{6241} a^{5} - \frac{32872401}{6241} a^{4} - \frac{299952853}{6241} a^{3} - \frac{43679966}{6241} a^{2} + \frac{184021220}{6241} a + \frac{49751343}{6241} \) |
\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 2\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 2 a + 3\) , \( -4 a^{5} + 7 a^{4} + 6 a^{3} - 19 a^{2} + 5 a + 2\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-3a+1\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+2a+3\right){x}-4a^{5}+7a^{4}+6a^{3}-19a^{2}+5a+2$ |
| 79.2-b4 |
79.2-b |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{16} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.803521265$ |
$61.76757866$ |
3.90207 |
\( -\frac{20536423248309805551373719264475252001}{2301619141096101839813550846721} a^{5} + \frac{42286471199890707532596245430877004817}{2301619141096101839813550846721} a^{4} + \frac{85829937322590393265081799820181353638}{2301619141096101839813550846721} a^{3} - \frac{151435862051147885670604858955956907747}{2301619141096101839813550846721} a^{2} - \frac{59339270938265465175658152496220093287}{2301619141096101839813550846721} a + \frac{85633195042831977374230614370327142872}{2301619141096101839813550846721} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( 129 a^{5} - 153 a^{4} - 413 a^{3} - 77 a^{2} + 214 a + 55\) , \( -49 a^{5} - 1470 a^{4} + 3363 a^{3} + 2379 a^{2} - 2233 a - 727\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a+1\right){x}^{2}+\left(129a^{5}-153a^{4}-413a^{3}-77a^{2}+214a+55\right){x}-49a^{5}-1470a^{4}+3363a^{3}+2379a^{2}-2233a-727$ |
| 79.2-b5 |
79.2-b |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{8} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$5.607042530$ |
$247.0703146$ |
3.90207 |
\( -\frac{59945977642839959955296974205}{1517108809906561} a^{5} + \frac{213782112253497340510376468222}{1517108809906561} a^{4} - \frac{95051328314657886465407000979}{1517108809906561} a^{3} - \frac{210802572721140186054803683068}{1517108809906561} a^{2} + \frac{90384715308208117615443548950}{1517108809906561} a + \frac{38273755986660551566870677480}{1517108809906561} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 18 a^{2} - a - 5\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 2\) , \( -29 a^{5} + 70 a^{4} + 70 a^{3} - 167 a^{2} + 3 a - 12\) , \( -79 a^{5} + 156 a^{4} + 284 a^{3} - 398 a^{2} - 206 a + 60\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+a+2\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+4a+2\right){y}={x}^{3}+\left(3a^{5}-7a^{4}-8a^{3}+18a^{2}-a-5\right){x}^{2}+\left(-29a^{5}+70a^{4}+70a^{3}-167a^{2}+3a-12\right){x}-79a^{5}+156a^{4}+284a^{3}-398a^{2}-206a+60$ |
| 79.2-b6 |
79.2-b |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{4} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$11.21408506$ |
$3.860473666$ |
3.90207 |
\( -\frac{1619387187484867716323758220255428895}{38950081} a^{5} + \frac{5775131325516164163000920397685702191}{38950081} a^{4} - \frac{2567721331850346841752822599008536358}{38950081} a^{3} - \frac{5694642641430730724330927372663821277}{38950081} a^{2} + \frac{2441656339550899995382491638454955943}{38950081} a + \frac{1033929732337466317153730367224460792}{38950081} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 18 a^{2} - a - 5\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 2\) , \( -109 a^{5} - 25 a^{4} + 885 a^{3} + 248 a^{2} - 1442 a - 352\) , \( -1333 a^{5} - 59 a^{4} + 10226 a^{3} + 2368 a^{2} - 16307 a - 4282\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+a+2\right){x}{y}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+4a+2\right){y}={x}^{3}+\left(3a^{5}-7a^{4}-8a^{3}+18a^{2}-a-5\right){x}^{2}+\left(-109a^{5}-25a^{4}+885a^{3}+248a^{2}-1442a-352\right){x}-1333a^{5}-59a^{4}+10226a^{3}+2368a^{2}-16307a-4282$ |
| 79.2-c1 |
79.2-c |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4561.989725$ |
2.14162 |
\( -\frac{23056887399498782353187}{6241} a^{5} + \frac{12282118445872874540738}{6241} a^{4} + \frac{110249254127088991226931}{6241} a^{3} + \frac{23428771302249586031484}{6241} a^{2} - \frac{57850223421360506122838}{6241} a - \frac{15713686931776062246680}{6241} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 4\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 7 a - 2\) , \( 0\) , \( 15 a^{5} - 10 a^{4} - 95 a^{3} + 20 a^{2} + 110 a - 44\) , \( -52 a^{5} + 21 a^{4} + 355 a^{3} - 28 a^{2} - 413 a + 161\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+4\right){x}{y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+3a^{2}+7a-2\right){x}^{2}+\left(15a^{5}-10a^{4}-95a^{3}+20a^{2}+110a-44\right){x}-52a^{5}+21a^{4}+355a^{3}-28a^{2}-413a+161$ |
| 79.2-c2 |
79.2-c |
$6$ |
$8$ |
6.6.1134389.1 |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{4} \) |
$136.97936$ |
$(-a^5+a^4+4a^3+a^2-3a-5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$18247.95890$ |
2.14162 |
\( -\frac{25578474509197103}{38950081} a^{5} + \frac{13769208943393063}{38950081} a^{4} + \frac{122006081712216622}{38950081} a^{3} + \frac{25777818166571072}{38950081} a^{2} - \frac{63987895436719587}{38950081} a - \frac{17369745196758095}{38950081} \) |
\( \bigl[-a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 4\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 7 a - 2\) , \( 0\) , \( -4\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 4 a^{2} - 22 a\bigr] \) |
${y}^2+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+4\right){x}{y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+3a^{2}+7a-2\right){x}^{2}-4{x}-3a^{5}+2a^{4}+19a^{3}-4a^{2}-22a$ |
*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.
