| 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 |
| 11.1-a1 |
11.1-a |
$2$ |
$5$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{5} \) |
$47.30901$ |
$(a^3-2a^2-4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$100$ |
\( 5 \) |
$1$ |
$1.423989881$ |
1.70927090 |
\( \frac{1126246945288183337113600000}{161051} a^{4} - \frac{3167750245713548570092343296}{161051} a^{3} - \frac{3056929369939424158290743296}{161051} a^{2} + \frac{5862986448443189381528686592}{161051} a - \frac{1385876399272941242892767232}{161051} \) |
\( \bigl[0\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 5 a\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 3\) , \( 406 a^{4} - 355 a^{3} - 2717 a^{2} - 1075 a + 547\) , \( 8131 a^{4} - 8325 a^{3} - 51171 a^{2} - 19170 a + 10178\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-11a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-5a\right){x}^{2}+\left(406a^{4}-355a^{3}-2717a^{2}-1075a+547\right){x}+8131a^{4}-8325a^{3}-51171a^{2}-19170a+10178$ |
| 11.1-a2 |
11.1-a |
$2$ |
$5$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$47.30901$ |
$(a^3-2a^2-4a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$4449.968380$ |
1.70927090 |
\( \frac{5331451904}{11} a^{4} + \frac{6343421952}{11} a^{3} - \frac{6421852160}{11} a^{2} - \frac{4489752576}{11} a + \frac{1671270400}{11} \) |
\( \bigl[0\) , \( -a^{2} + 3 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + a + 1\) , \( -2 a^{2} + 5 a + 5\) , \( 4 a^{4} - 9 a^{3} - 16 a^{2} + 9 a + 11\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+a+1\right){y}={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(-2a^{2}+5a+5\right){x}+4a^{4}-9a^{3}-16a^{2}+9a+11$ |
| 11.1-b1 |
11.1-b |
$2$ |
$3$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$47.30901$ |
$(a^3-2a^2-4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.014438820$ |
$15874.55089$ |
2.75129500 |
\( -\frac{283497287680}{1331} a^{4} + \frac{483768332288}{1331} a^{3} + \frac{1559519793152}{1331} a^{2} - \frac{392704233472}{1331} a - \frac{965786435584}{1331} \) |
\( \bigl[0\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 2\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} - a^{2} + 2\) , \( a^{4} - 4 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+4a+2\right){x}^{2}+\left(-a^{3}-a^{2}+2\right){x}+a^{4}-4a^{2}-a+1$ |
| 11.1-b2 |
11.1-b |
$2$ |
$3$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$47.30901$ |
$(a^3-2a^2-4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.043316461$ |
$5291.516965$ |
2.75129500 |
\( \frac{3551232}{11} a^{4} - \frac{4059136}{11} a^{3} - \frac{20672512}{11} a^{2} - \frac{7303168}{11} a + \frac{3997696}{11} \) |
\( \bigl[0\) , \( a\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 2\) , \( a^{4} - a^{3} - 6 a^{2} - 3 a + 1\) , \( -a^{4} + a^{3} + 6 a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+a{x}^{2}+\left(a^{4}-a^{3}-6a^{2}-3a+1\right){x}-a^{4}+a^{3}+6a^{2}+3a-3$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
13.1 |
\( 13 \) |
\( -13 \) |
$48.10596$ |
$(a^4-2a^3-4a^2+2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.046565842$ |
$6127.027696$ |
3.42469031 |
\( \frac{7838}{13} a^{4} - \frac{34674}{13} a^{3} + \frac{16604}{13} a^{2} + \frac{50283}{13} a - \frac{10993}{13} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 2 a - 3\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 2\) , \( 2 a^{4} - a^{3} - 16 a^{2} - 4 a + 15\) , \( -18 a^{4} + 33 a^{3} + 94 a^{2} - 32 a - 53\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-2a-3\right){x}^{2}+\left(2a^{4}-a^{3}-16a^{2}-4a+15\right){x}-18a^{4}+33a^{3}+94a^{2}-32a-53$ |
| 17.1-a1 |
17.1-a |
$4$ |
$4$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$49.41394$ |
$(a^4-2a^3-5a^2+a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 3 \) |
$1$ |
$81.34513676$ |
2.34340218 |
\( -\frac{748091530434667636578}{4913} a^{4} + \frac{1421573337562211219}{4913} a^{3} + \frac{6749485955891272736468}{4913} a^{2} + \frac{3213104074201698561220}{4913} a - \frac{1519269203416467592115}{4913} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} - a + 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 3\) , \( -117 a^{4} + 514 a^{3} - 318 a^{2} - 464 a + 141\) , \( 3080 a^{4} - 10419 a^{3} + 42 a^{2} + 6443 a - 1697\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}-a+4\right){x}^{2}+\left(-117a^{4}+514a^{3}-318a^{2}-464a+141\right){x}+3080a^{4}-10419a^{3}+42a^{2}+6443a-1697$ |
| 17.1-a2 |
17.1-a |
$4$ |
$4$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$49.41394$ |
$(a^4-2a^3-5a^2+a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$650.7610941$ |
2.34340218 |
\( -\frac{3015149053665871}{24137569} a^{4} - \frac{764713166787431}{24137569} a^{3} + \frac{28972470067066415}{24137569} a^{2} + \frac{15096145370756503}{24137569} a - \frac{5961152725283797}{24137569} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} - a + 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 3\) , \( -12 a^{4} + 39 a^{3} + 7 a^{2} - 29 a - 4\) , \( 28 a^{4} - 120 a^{3} + 80 a^{2} + 78 a - 69\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}-a+4\right){x}^{2}+\left(-12a^{4}+39a^{3}+7a^{2}-29a-4\right){x}+28a^{4}-120a^{3}+80a^{2}+78a-69$ |
| 17.1-a3 |
17.1-a |
$4$ |
$4$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$49.41394$ |
$(a^4-2a^3-5a^2+a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$5206.088752$ |
2.34340218 |
\( \frac{3152928700}{4913} a^{4} + \frac{3847598114}{4913} a^{3} - \frac{3707442708}{4913} a^{2} - \frac{2630270281}{4913} a + \frac{1005064926}{4913} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} - a + 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 3\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} + a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2}\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}-a+4\right){x}^{2}+\left(-2a^{4}+4a^{3}+7a^{2}+a+1\right){x}+a^{4}-2a^{3}-4a^{2}$ |
| 17.1-a4 |
17.1-a |
$4$ |
$4$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{12} \) |
$49.41394$ |
$(a^4-2a^3-5a^2+a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$20.33628419$ |
2.34340218 |
\( \frac{259021353377415701563595810434}{582622237229761} a^{4} - \frac{442008173043065659687822475843}{582622237229761} a^{3} - \frac{1424856245421232494725929043476}{582622237229761} a^{2} + \frac{358804027431106347098250138876}{582622237229761} a + \frac{882389344100608701328610522675}{582622237229761} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} - a + 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 3\) , \( -67 a^{4} + 124 a^{3} + 332 a^{2} - 74 a - 229\) , \( -436 a^{4} + 647 a^{3} + 2694 a^{2} - 475 a - 1757\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}-a+4\right){x}^{2}+\left(-67a^{4}+124a^{3}+332a^{2}-74a-229\right){x}-436a^{4}+647a^{3}+2694a^{2}-475a-1757$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$49.96661$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1054.752232$ |
2.53212093 |
\( \frac{18624273}{19} a^{4} - \frac{65739508}{19} a^{3} + \frac{7452735}{19} a^{2} + \frac{44466694}{19} a - \frac{12166923}{19} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 3\) , \( a^{2} - 2 a - 2\) , \( a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( -2 a^{4} + 4 a^{3} + 10 a^{2} - 4 a - 5\) , \( 2 a^{4} - 17 a^{2} - 10 a + 2\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+4a+3\right){x}{y}+\left(a^{4}-a^{3}-7a^{2}-a+4\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-2a^{4}+4a^{3}+10a^{2}-4a-5\right){x}+2a^{4}-17a^{2}-10a+2$ |
| 23.1-a1 |
23.1-a |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$50.93043$ |
$(-2a^4+4a^3+9a^2-3a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$3842.881666$ |
2.30638078 |
\( -\frac{84335536492}{23} a^{4} + \frac{203202436164}{23} a^{3} + \frac{723526606403}{23} a^{2} + \frac{239674570700}{23} a - \frac{137214499184}{23} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{4} - a^{3} - 6 a^{2} - 4 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( -47 a^{4} + 80 a^{3} + 255 a^{2} - 55 a - 151\) , \( 116 a^{4} - 202 a^{3} - 623 a^{2} + 157 a + 379\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-4a+1\right){x}^{2}+\left(-47a^{4}+80a^{3}+255a^{2}-55a-151\right){x}+116a^{4}-202a^{3}-623a^{2}+157a+379$ |
| 23.1-a2 |
23.1-a |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$50.93043$ |
$(-2a^4+4a^3+9a^2-3a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$1280.960555$ |
2.30638078 |
\( -\frac{25145957723}{12167} a^{4} + \frac{83642378438}{12167} a^{3} + \frac{35717280314}{12167} a^{2} - \frac{175492735257}{12167} a + \frac{85115760257}{12167} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 2 a + 3\) , \( 2 a^{4} - 4 a^{3} - 9 a^{2} + 4 a + 2\) , \( -2 a^{4} - 8 a^{3} + 49 a^{2} + a - 33\) , \( -81 a^{4} + 210 a^{3} + 213 a^{2} - 150 a - 119\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(2a^{4}-4a^{3}-9a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+2a+3\right){x}^{2}+\left(-2a^{4}-8a^{3}+49a^{2}+a-33\right){x}-81a^{4}+210a^{3}+213a^{2}-150a-119$ |
| 23.1-a3 |
23.1-a |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23^{6} \) |
$50.93043$ |
$(-2a^4+4a^3+9a^2-3a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$160.1200694$ |
2.30638078 |
\( \frac{450984274925453037813}{148035889} a^{4} - \frac{769584044807401362321}{148035889} a^{3} - \frac{2480829088119184461168}{148035889} a^{2} + \frac{624716635697263463929}{148035889} a + \frac{1536335420071798055438}{148035889} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + a\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 2\) , \( -28 a^{4} + 33 a^{3} + 187 a^{2} + 17 a - 139\) , \( -150 a^{4} + 216 a^{3} + 928 a^{2} - 61 a - 671\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+a\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(-28a^{4}+33a^{3}+187a^{2}+17a-139\right){x}-150a^{4}+216a^{3}+928a^{2}-61a-671$ |
| 23.1-a4 |
23.1-a |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$50.93043$ |
$(-2a^4+4a^3+9a^2-3a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$480.3602083$ |
2.30638078 |
\( \frac{268643458694519442765786}{529} a^{4} + \frac{319648670954419378419480}{529} a^{3} - \frac{323582111441201150241986}{529} a^{2} - \frac{226251938694468107910169}{529} a + \frac{84217890913906831627260}{529} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{4} - a^{3} - 6 a^{2} - 4 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( -282 a^{4} + 520 a^{3} + 1420 a^{2} - 405 a - 861\) , \( -2802 a^{4} + 4534 a^{3} + 16223 a^{2} - 3754 a - 10106\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-4a+1\right){x}^{2}+\left(-282a^{4}+520a^{3}+1420a^{2}-405a-861\right){x}-2802a^{4}+4534a^{3}+16223a^{2}-3754a-10106$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$50.93043$ |
$(-2a^4+4a^3+9a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.055658351$ |
$20736.44261$ |
3.46344741 |
\( -\frac{492525}{23} a^{4} + \frac{767617}{23} a^{3} + \frac{2470975}{23} a^{2} + \frac{303842}{23} a + \frac{26865}{23} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 3\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 2 a^{4} - 4 a^{3} - 8 a^{2} + 2 a\) , \( -a^{4} - 3 a^{3} + 14 a^{2} + 19 a - 7\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-1\right){x}^{2}+\left(2a^{4}-4a^{3}-8a^{2}+2a\right){x}-a^{4}-3a^{3}+14a^{2}+19a-7$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$50.93043$ |
$(-2a^4+4a^3+9a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.111316703$ |
$5184.110653$ |
3.46344741 |
\( -\frac{77686929839}{529} a^{4} + \frac{253764069142}{529} a^{3} + \frac{123408931883}{529} a^{2} - \frac{531012001595}{529} a + \frac{246528725004}{529} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 3\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 17 a^{4} - 49 a^{3} - 43 a^{2} + 92 a - 25\) , \( 82 a^{4} - 237 a^{3} - 211 a^{2} + 455 a - 107\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-1\right){x}^{2}+\left(17a^{4}-49a^{3}-43a^{2}+92a-25\right){x}+82a^{4}-237a^{3}-211a^{2}+455a-107$ |
| 23.2-a1 |
23.2-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( 23^{3} \) |
$50.93043$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.037450081$ |
$8453.608557$ |
3.80013382 |
\( \frac{2045977821}{12167} a^{4} - \frac{147693574}{529} a^{3} - \frac{11142704250}{12167} a^{2} + \frac{1807554497}{12167} a + \frac{6091169125}{12167} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( a + 1\) , \( a^{4} - a^{3} - 7 a^{2} + 4\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - a - 5\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{4}-a^{3}-7a^{2}+4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a^{4}+3a^{3}+9a^{2}-a-5\right){x}-a^{4}+2a^{3}+5a^{2}-a-3$ |
| 23.2-b1 |
23.2-b |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$50.93043$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.016670988$ |
$19275.90526$ |
3.85727076 |
\( \frac{18122264358}{23} a^{4} - 1342750814 a^{3} - \frac{99713128787}{23} a^{2} + \frac{24870351901}{23} a + \frac{61584243507}{23} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 3\) , \( 7 a^{4} - 14 a^{3} - 31 a^{2} + 14 a + 2\) , \( -17 a^{4} + 27 a^{3} + 86 a^{2} + 4 a - 8\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+3a+2\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+a+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}+4\right){x}^{2}+\left(7a^{4}-14a^{3}-31a^{2}+14a+2\right){x}-17a^{4}+27a^{3}+86a^{2}+4a-8$ |
| 31.1-a1 |
31.1-a |
$2$ |
$3$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.090539176$ |
$3698.155078$ |
4.01907078 |
\( -\frac{300817675036766}{31} a^{4} + \frac{343221210476202}{31} a^{3} + \frac{1798928808970093}{31} a^{2} + 20738617052351 a - \frac{350179265555711}{31} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 160 a^{4} - 183 a^{3} - 955 a^{2} - 339 a + 186\) , \( -1951 a^{4} + 2227 a^{3} + 11666 a^{2} + 4166 a - 2270\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(160a^{4}-183a^{3}-955a^{2}-339a+186\right){x}-1951a^{4}+2227a^{3}+11666a^{2}+4166a-2270$ |
| 31.1-a2 |
31.1-a |
$2$ |
$3$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31^{3} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.030179725$ |
$11094.46523$ |
4.01907078 |
\( \frac{2224846511719}{29791} a^{4} - \frac{7307102837938}{29791} a^{3} - \frac{6433769518685}{29791} a^{2} + \frac{424797908991}{961} a - \frac{3142956624467}{29791} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 5 a + 3\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 5 a - 1\) , \( a^{4} - a^{3} - 7 a^{2} + 4\) , \( -7 a^{4} + 17 a^{3} + 26 a^{2} - 31 a\) , \( -5 a^{3} + 20 a^{2} - 14 a\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+5a+3\right){x}{y}+\left(a^{4}-a^{3}-7a^{2}+4\right){y}={x}^{3}+\left(-2a^{4}+4a^{3}+9a^{2}-5a-1\right){x}^{2}+\left(-7a^{4}+17a^{3}+26a^{2}-31a\right){x}-5a^{3}+20a^{2}-14a$ |
| 31.1-b1 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$2.490935609$ |
$535.5049579$ |
4.00285631 |
\( \frac{113072043240307986346277}{29791} a^{4} - \frac{399120131288890886869227}{29791} a^{3} + \frac{45208236860988537442792}{29791} a^{2} + \frac{8711522355511940632044}{961} a - \frac{73913626654323074142044}{29791} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 170 a^{4} - 282 a^{3} - 961 a^{2} + 191 a + 590\) , \( -1084 a^{4} + 1856 a^{3} + 5975 a^{2} - 1508 a - 3702\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-2a-1\right){x}^{2}+\left(170a^{4}-282a^{3}-961a^{2}+191a+590\right){x}-1084a^{4}+1856a^{3}+5975a^{2}-1508a-3702$ |
| 31.1-b2 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{12} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$2.490935609$ |
$66.93811974$ |
4.00285631 |
\( -\frac{1568542757885405624737876091}{787662783788549761} a^{4} + \frac{1789239850643007905719969653}{787662783788549761} a^{3} + \frac{9380454077947561271500795112}{787662783788549761} a^{2} + \frac{108216683576570822067967084}{25408476896404831} a - \frac{1824368553931963427157137932}{787662783788549761} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 4 a + 2\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 5 a - 1\) , \( a^{4} - a^{3} - 7 a^{2} + 3\) , \( -48 a^{4} + 140 a^{3} + 117 a^{2} - 258 a + 54\) , \( 533 a^{4} - 1493 a^{3} - 1449 a^{2} + 2717 a - 650\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-7a^{2}+3\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+5a-1\right){x}^{2}+\left(-48a^{4}+140a^{3}+117a^{2}-258a+54\right){x}+533a^{4}-1493a^{3}-1449a^{2}+2717a-650$ |
| 31.1-b3 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1.245467804$ |
$2142.019831$ |
4.00285631 |
\( \frac{450317313215790441}{887503681} a^{4} - \frac{1589526193748969780}{887503681} a^{3} + \frac{180141777441504435}{887503681} a^{2} + \frac{34695821211951721}{28629151} a - \frac{294386506665216499}{887503681} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} + 3\) , \( -a^{4} + a^{3} + 7 a^{2} + 2 a - 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 3\) , \( 283 a^{4} - 324 a^{3} - 1690 a^{2} - 602 a + 325\) , \( 4605 a^{4} - 5254 a^{3} - 27538 a^{2} - 9843 a + 5358\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}+3\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+7a^{2}+2a-4\right){x}^{2}+\left(283a^{4}-324a^{3}-1690a^{2}-602a+325\right){x}+4605a^{4}-5254a^{3}-27538a^{2}-9843a+5358$ |
| 31.1-b4 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.622733902$ |
$8568.079327$ |
4.00285631 |
\( \frac{134559173}{29791} a^{4} + \frac{155249897}{29791} a^{3} - \frac{1937634179}{29791} a^{2} - \frac{7304516}{961} a + \frac{1452524916}{29791} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} + 3\) , \( -a^{4} + a^{3} + 7 a^{2} + 2 a - 4\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 3\) , \( 3 a^{4} - 4 a^{3} - 15 a^{2} - 7 a\) , \( 165 a^{4} - 188 a^{3} - 986 a^{2} - 356 a + 190\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}+3\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+7a^{2}+2a-4\right){x}^{2}+\left(3a^{4}-4a^{3}-15a^{2}-7a\right){x}+165a^{4}-188a^{3}-986a^{2}-356a+190$ |
| 31.1-b5 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.868201706$ |
$2856.026442$ |
4.00285631 |
\( -\frac{1458273}{31} a^{4} + \frac{4843278}{31} a^{3} + \frac{2093789}{31} a^{2} - 327854 a + \frac{4909743}{31} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 11 a^{2} + a + 4\) , \( -2 a^{4} + 5 a^{3} + 7 a^{2} - 8 a - 1\) , \( a^{4} - a^{3} - 6 a^{2} - 3 a + 1\) , \( -12 a^{4} + 19 a^{3} + 62 a^{2} + 3 a - 6\) , \( -539 a^{4} + 619 a^{3} + 3216 a^{2} + 1135 a - 622\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-11a^{2}+a+4\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}-3a+1\right){y}={x}^{3}+\left(-2a^{4}+5a^{3}+7a^{2}-8a-1\right){x}^{2}+\left(-12a^{4}+19a^{3}+62a^{2}+3a-6\right){x}-539a^{4}+619a^{3}+3216a^{2}+1135a-622$ |
| 31.1-b6 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$3.736403413$ |
$714.0066106$ |
4.00285631 |
\( -\frac{22570115072000}{961} a^{4} + \frac{65095784734216}{961} a^{3} + \frac{57196070281767}{961} a^{2} - \frac{3969943339535}{31} a + \frac{34537745898823}{961} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} + 4\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 6 a + 1\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 3\) , \( 275 a^{4} - 314 a^{3} - 1647 a^{2} - 585 a + 325\) , \( -3611 a^{4} + 4119 a^{3} + 21594 a^{2} + 7723 a - 4201\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}+4\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-3a^{3}-3a^{2}+6a+1\right){x}^{2}+\left(275a^{4}-314a^{3}-1647a^{2}-585a+325\right){x}-3611a^{4}+4119a^{3}+21594a^{2}+7723a-4201$ |
| 31.1-b7 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{4} \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$7.472806827$ |
$22.31270658$ |
4.00285631 |
\( \frac{7030102092475686434734469}{923521} a^{4} - \frac{11996549884866855701497225}{923521} a^{3} - \frac{38672042785866399317533337}{923521} a^{2} + \frac{314138873473712053399288}{29791} a + \frac{23948941171307125067661552}{923521} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + a\) , \( -a^{4} + a^{3} + 6 a^{2} + 3 a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( -3 a^{4} + 10 a^{3} - 25 a^{2} + 69 a - 22\) , \( -23 a^{4} + 125 a^{3} - 232 a^{2} + 198 a - 47\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+a\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}+3a\right){x}^{2}+\left(-3a^{4}+10a^{3}-25a^{2}+69a-22\right){x}-23a^{4}+125a^{3}-232a^{2}+198a-47$ |
| 31.1-b8 |
31.1-b |
$8$ |
$12$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$7.472806827$ |
$178.5016526$ |
4.00285631 |
\( -\frac{102874088330653810959515}{31} a^{4} + \frac{289349880090494972415767}{31} a^{3} + \frac{279227236448408494590983}{31} a^{2} - 17275458000288067908616 a + \frac{126589263325540728688416}{31} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - 3 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 2 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 31 a^{4} - 18 a^{3} - 203 a^{2} - 175 a - 34\) , \( -377 a^{4} + 497 a^{3} + 2210 a^{2} + 393 a - 719\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-3a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-2a\right){x}^{2}+\left(31a^{4}-18a^{3}-203a^{2}-175a-34\right){x}-377a^{4}+497a^{3}+2210a^{2}+393a-719$ |
| 31.1-c1 |
31.1-c |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$52.47358$ |
$(-a^3+2a^2+5a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.141168327$ |
$2490.156681$ |
4.21956750 |
\( -\frac{947203}{31} a^{4} + \frac{2425137}{31} a^{3} + \frac{588424}{31} a^{2} - 12683 a - \frac{125141}{31} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - 2 a + 1\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( -2 a^{4} + 8 a^{2} + 4 a\) , \( 2 a^{4} + 2 a^{3} - 3 a^{2} - 2 a\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-2a+1\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-3a-2\right){x}^{2}+\left(-2a^{4}+8a^{2}+4a\right){x}+2a^{4}+2a^{3}-3a^{2}-2a$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{15} \) |
$52.64045$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.008906187$ |
$3524.165535$ |
5.65123513 |
\( -4454434 a^{4} + \frac{31447351}{2} a^{3} - \frac{14257345}{8} a^{2} - \frac{85124199}{8} a + \frac{23312477}{8} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} + 3\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 1\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 4\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}+3\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+4a+1\right){x}^{2}+\left(a^{3}-2a^{2}-4a+2\right){x}$ |
| 41.1-a1 |
41.1-a |
$2$ |
$5$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$53.96137$ |
$(a^4-3a^3-2a^2+5a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$5774.492209$ |
2.21803182 |
\( \frac{34815}{41} a^{4} - \frac{83204}{41} a^{3} - \frac{124888}{41} a^{2} + \frac{139624}{41} a + \frac{41398}{41} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - 3 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} - 4 a + 3\) , \( -2 a^{4} + 7 a^{3} - a^{2} - 5 a + 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-3a+2\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}^{2}+\left(a^{4}-2a^{3}-3a^{2}-4a+3\right){x}-2a^{4}+7a^{3}-a^{2}-5a+1$ |
| 41.1-a2 |
41.1-a |
$2$ |
$5$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41^{5} \) |
$53.96137$ |
$(a^4-3a^3-2a^2+5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$100$ |
\( 5 \) |
$1$ |
$1.847837507$ |
2.21803182 |
\( \frac{35634410896057629224902}{115856201} a^{4} + \frac{42400063820921246918995}{115856201} a^{3} - \frac{42921798303347961365331}{115856201} a^{2} - \frac{30011375974528753844093}{115856201} a + \frac{11171149997353979332294}{115856201} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} + 3\) , \( -a^{4} + a^{3} + 6 a^{2} + 4 a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( 32 a^{4} - 54 a^{3} - 163 a^{2} - 6 a + 1\) , \( 412 a^{4} - 779 a^{3} - 1901 a^{2} + 399 a + 12\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}+4a\right){x}^{2}+\left(32a^{4}-54a^{3}-163a^{2}-6a+1\right){x}+412a^{4}-779a^{3}-1901a^{2}+399a+12$ |
| 41.1-b1 |
41.1-b |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$53.96137$ |
$(a^4-3a^3-2a^2+5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$886.9936938$ |
2.12938663 |
\( -\frac{48426850}{41} a^{4} + \frac{37141191}{41} a^{3} + \frac{325347528}{41} a^{2} + \frac{182449187}{41} a - \frac{84032601}{41} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{2} + 2 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 5 a + 4\) , \( 2 a^{4} - a^{3} - 6 a^{2} + 2 a + 2\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(2a^{4}-3a^{3}-7a^{2}+5a+4\right){x}+2a^{4}-a^{3}-6a^{2}+2a+2$ |
| 43.1-a1 |
43.1-a |
$2$ |
$3$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( - 43^{3} \) |
$54.21899$ |
$(a^4-a^3-7a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.078808965$ |
$5151.775917$ |
4.87345080 |
\( -\frac{13307863458}{79507} a^{4} - \frac{17958390449}{79507} a^{3} + \frac{353981003}{1849} a^{2} + \frac{14411541113}{79507} a - \frac{4979446304}{79507} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a\) , \( 2 a^{4} - 7 a^{3} - 3 a^{2} + 15 a - 3\) , \( -a^{4} + 3 a^{3} + a^{2} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+4a+2\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-a\right){x}^{2}+\left(2a^{4}-7a^{3}-3a^{2}+15a-3\right){x}-a^{4}+3a^{3}+a^{2}-3a+1$ |
| 43.1-a2 |
43.1-a |
$2$ |
$3$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
43.1 |
\( 43 \) |
\( -43 \) |
$54.21899$ |
$(a^4-a^3-7a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.236426896$ |
$1717.258639$ |
4.87345080 |
\( \frac{18554110}{43} a^{4} - \frac{7259321}{43} a^{3} - 3443970 a^{2} - \frac{66058974}{43} a + \frac{32192557}{43} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 11 a^{2} + a + 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 4 a + 1\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 3\) , \( 2 a^{3} - 2 a^{2} - 9 a + 2\) , \( a^{4} + 4 a^{3} - 5 a^{2} - 10 a + 3\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-11a^{2}+a+4\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-4a+1\right){x}^{2}+\left(2a^{3}-2a^{2}-9a+2\right){x}+a^{4}+4a^{3}-5a^{2}-10a+3$ |
| 47.1-a1 |
47.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47^{3} \) |
$54.70340$ |
$(a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.193393007$ |
$1966.684110$ |
4.56540565 |
\( \frac{67070385032}{103823} a^{4} - \frac{188466866576}{103823} a^{3} - \frac{182717875487}{103823} a^{2} + \frac{349548017880}{103823} a - \frac{82595559200}{103823} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 4 a + 3\) , \( a^{4} - a^{3} - 6 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 2 a + 2\) , \( a^{4} - a^{3} - 6 a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-2a+1\right){x}^{2}+\left(2a+2\right){x}+a^{4}-a^{3}-6a^{2}-2a+1$ |
| 47.1-b1 |
47.1-b |
$2$ |
$2$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$54.70340$ |
$(a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$543.2102351$ |
2.93416446 |
\( -\frac{564740706501}{47} a^{4} + \frac{1753407469078}{47} a^{3} + \frac{1117216187091}{47} a^{2} - \frac{3509680542708}{47} a + \frac{1386653634976}{47} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 2\) , \( a^{4} - a^{3} - 6 a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 7 a^{2} - a + 3\) , \( 4 a^{4} - 8 a^{3} - 28 a^{2} - 7 a + 2\) , \( -17 a^{3} - 26 a^{2} + 2 a + 1\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+3a+2\right){x}{y}+\left(a^{4}-a^{3}-7a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-3a+1\right){x}^{2}+\left(4a^{4}-8a^{3}-28a^{2}-7a+2\right){x}-17a^{3}-26a^{2}+2a+1$ |
| 47.1-b2 |
47.1-b |
$2$ |
$2$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{2} \) |
$54.70340$ |
$(a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$36$ |
\( 2 \) |
$1$ |
$67.90127939$ |
2.93416446 |
\( -\frac{2705176821564539734621306}{2209} a^{4} + \frac{7608743869763071400966062}{2209} a^{3} + \frac{7342558852739233282001795}{2209} a^{2} - \frac{14082537682732125600617991}{2209} a + \frac{3328791015931477857190574}{2209} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + a + 1\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 4 a - 1\) , \( a + 1\) , \( -37 a^{4} - 44 a^{3} + 549 a^{2} + 6 a - 357\) , \( 971 a^{4} - 2219 a^{3} - 3523 a^{2} + 1651 a + 2056\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{4}+4a^{3}+9a^{2}-4a-1\right){x}^{2}+\left(-37a^{4}-44a^{3}+549a^{2}+6a-357\right){x}+971a^{4}-2219a^{3}-3523a^{2}+1651a+2056$ |
| 47.1-c1 |
47.1-c |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$54.70340$ |
$(a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.575417161$ |
$670.0415349$ |
4.62794864 |
\( \frac{412686053817}{47} a^{4} - \frac{470858644354}{47} a^{3} - \frac{2467916283377}{47} a^{2} - \frac{881978376410}{47} a + \frac{480404369141}{47} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 4 a + 2\) , \( 2 a^{4} - 4 a^{3} - 9 a^{2} + 4 a + 3\) , \( a + 1\) , \( 2 a^{4} - 3 a^{3} - 12 a^{2} + 7\) , \( 2 a^{4} - 3 a^{3} - 12 a^{2} - a + 5\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+4a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{4}-4a^{3}-9a^{2}+4a+3\right){x}^{2}+\left(2a^{4}-3a^{3}-12a^{2}+7\right){x}+2a^{4}-3a^{3}-12a^{2}-a+5$ |
| 47.1-d1 |
47.1-d |
$2$ |
$2$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{3} \) |
$54.70340$ |
$(a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$1435.807301$ |
2.58518371 |
\( -\frac{11716811400}{103823} a^{4} + \frac{4210989889}{103823} a^{3} + \frac{51831149002}{103823} a^{2} + \frac{21813915639}{103823} a - \frac{8499133584}{103823} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{4} - a^{3} - 6 a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 3\) , \( 7 a^{4} - 9 a^{3} - 38 a^{2} - 10 a + 5\) , \( -27 a^{4} + 30 a^{3} + 165 a^{2} + 64 a - 35\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-3a+2\right){x}^{2}+\left(7a^{4}-9a^{3}-38a^{2}-10a+5\right){x}-27a^{4}+30a^{3}+165a^{2}+64a-35$ |
| 47.1-d2 |
47.1-d |
$2$ |
$2$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{6} \) |
$54.70340$ |
$(a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$179.4759126$ |
2.58518371 |
\( \frac{1867587827374836692064}{10779215329} a^{4} + \frac{2222171319260606146479}{10779215329} a^{3} - \frac{2249516719921581981045}{10779215329} a^{2} - \frac{1572884922741399975897}{10779215329} a + \frac{585475903813763851658}{10779215329} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{4} - a^{3} - 6 a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 3\) , \( 2 a^{4} + a^{3} - 18 a^{2} - 15 a + 5\) , \( -35 a^{4} + 37 a^{3} + 216 a^{2} + 86 a - 46\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+2a+1\right){x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-3a+2\right){x}^{2}+\left(2a^{4}+a^{3}-18a^{2}-15a+5\right){x}-35a^{4}+37a^{3}+216a^{2}+86a-46$ |
| 47.1-e1 |
47.1-e |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{2} \) |
$54.70340$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.840019564$ |
$923.1538268$ |
4.65411891 |
\( -\frac{324743921401497241325946}{2209} a^{4} + \frac{370520122485413860544254}{2209} a^{3} + \frac{1942010873108672410358236}{2209} a^{2} + \frac{694031474611540100233689}{2209} a - \frac{378031602965268911913900}{2209} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} - a + 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + a + 2\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -18 a^{4} + 71 a^{3} - 29 a^{2} - 52 a + 19\) , \( -133 a^{4} + 447 a^{3} + 5 a^{2} - 271 a + 70\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}-a+4\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}+a+2\right){x}^{2}+\left(-18a^{4}+71a^{3}-29a^{2}-52a+19\right){x}-133a^{4}+447a^{3}+5a^{2}-271a+70$ |
| 47.1-e2 |
47.1-e |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( -47 \) |
$54.70340$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.420009782$ |
$3692.615307$ |
4.65411891 |
\( -\frac{248506791784}{47} a^{4} + \frac{283735096012}{47} a^{3} + \frac{1485715000215}{47} a^{2} + \frac{530227942320}{47} a - \frac{288999962464}{47} \) |
\( \bigl[a^{4} - a^{3} - 7 a^{2} + 4\) , \( -2 a^{4} + 5 a^{3} + 7 a^{2} - 8 a - 2\) , \( a^{4} - a^{3} - 7 a^{2} - a + 3\) , \( -8 a^{4} + 22 a^{3} + 24 a^{2} - 23 a - 9\) , \( -7 a^{3} + 16 a^{2} - a - 9\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-7a^{2}+4\right){x}{y}+\left(a^{4}-a^{3}-7a^{2}-a+3\right){y}={x}^{3}+\left(-2a^{4}+5a^{3}+7a^{2}-8a-2\right){x}^{2}+\left(-8a^{4}+22a^{3}+24a^{2}-23a-9\right){x}-7a^{3}+16a^{2}-a-9$ |
| 47.1-e3 |
47.1-e |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{3} \) |
$54.70340$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.140003260$ |
$11077.84592$ |
4.65411891 |
\( \frac{294224708001177}{103823} a^{4} - \frac{1038460121005630}{103823} a^{3} + \frac{117344406243886}{103823} a^{2} + \frac{702666179595819}{103823} a - \frac{192129421942987}{103823} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 7 a\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 2\) , \( 27 a^{4} - 28 a^{3} - 167 a^{2} - 70 a + 36\) , \( -98 a^{4} + 113 a^{3} + 584 a^{2} + 204 a - 114\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}-3a+2\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a\right){x}^{2}+\left(27a^{4}-28a^{3}-167a^{2}-70a+36\right){x}-98a^{4}+113a^{3}+584a^{2}+204a-114$ |
| 47.1-e4 |
47.1-e |
$4$ |
$6$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{6} \) |
$54.70340$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.280006521$ |
$2769.461480$ |
4.65411891 |
\( \frac{8112384953343644131795}{10779215329} a^{4} - \frac{13843426371174100811879}{10779215329} a^{3} - \frac{44625585003909529109244}{10779215329} a^{2} + \frac{11237580899877754283129}{10779215329} a + \frac{27635916590732615854666}{10779215329} \) |
\( \bigl[a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 3\) , \( -2 a^{4} + 5 a^{3} + 7 a^{2} - 7 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a\) , \( -36 a^{4} + 84 a^{3} + 134 a^{2} - 100 a - 47\) , \( 42 a^{4} - 75 a^{3} - 192 a^{2} - 56 a + 214\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(-2a^{4}+5a^{3}+7a^{2}-7a-1\right){x}^{2}+\left(-36a^{4}+84a^{3}+134a^{2}-100a-47\right){x}+42a^{4}-75a^{3}-192a^{2}-56a+214$ |
| 53.1-a1 |
53.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
53.1 |
\( 53 \) |
\( 53 \) |
$55.36460$ |
$(a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1277.196746$ |
3.06613868 |
\( -\frac{28297004}{53} a^{4} + \frac{99406250}{53} a^{3} - \frac{10049631}{53} a^{2} - \frac{66656375}{53} a + \frac{18173433}{53} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( -a + 1\) , \( 2 a^{4} - 4 a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + 4 a^{3} + 4 a^{2} - 9 a + 1\) , \( -a^{4} + 4 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(2a^{4}-4a^{3}-9a^{2}+4a+3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{4}+4a^{3}+4a^{2}-9a+1\right){x}-a^{4}+4a^{2}-3$ |
| 53.1-b1 |
53.1-b |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
53.1 |
\( 53 \) |
\( 53 \) |
$55.36460$ |
$(a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.017412083$ |
$21360.57115$ |
4.46444630 |
\( \frac{16139425055}{53} a^{4} - \frac{18414215898}{53} a^{3} - \frac{96515393833}{53} a^{2} - \frac{34492585647}{53} a + \frac{18787577536}{53} \) |
\( \bigl[1\) , \( -a\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 4\) , \( -4 a^{4} + 7 a^{3} + 21 a^{2} - 4 a - 12\) , \( 11 a^{4} - 29 a^{3} - 26 a^{2} + 17 a + 11\bigr] \) |
${y}^2+{x}{y}+\left(2a^{4}-3a^{3}-11a^{2}+4\right){y}={x}^{3}-a{x}^{2}+\left(-4a^{4}+7a^{3}+21a^{2}-4a-12\right){x}+11a^{4}-29a^{3}-26a^{2}+17a+11$ |
| 79.1-a1 |
79.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
79.1 |
\( 79 \) |
\( 79 \) |
$57.61921$ |
$(2a^4-5a^3-7a^2+8a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.142136735$ |
$3014.057759$ |
5.14235320 |
\( -\frac{202618549}{79} a^{4} + \frac{569900237}{79} a^{3} + \frac{549964501}{79} a^{2} - \frac{1054794977}{79} a + \frac{249329548}{79} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + a\) , \( -a^{4} + a^{3} + 6 a^{2} + 4 a - 1\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 2\) , \( -4 a^{4} + 2 a^{3} + 30 a^{2} + 16 a - 7\) , \( -2 a^{4} + 18 a^{2} + 9 a - 6\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+a\right){x}{y}+\left(a^{4}-2a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}+4a-1\right){x}^{2}+\left(-4a^{4}+2a^{3}+30a^{2}+16a-7\right){x}-2a^{4}+18a^{2}+9a-6$ |
| 83.1-a1 |
83.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
83.1 |
\( 83 \) |
\( 83 \) |
$57.90451$ |
$(2a^4-4a^3-9a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.052544978$ |
$7932.287840$ |
5.00303658 |
\( -\frac{654601538}{83} a^{4} + \frac{2255376960}{83} a^{3} - \frac{21433300}{83} a^{2} - \frac{1782041095}{83} a + \frac{472762477}{83} \) |
\( \bigl[2 a^{4} - 4 a^{3} - 9 a^{2} + 5 a + 3\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 8 a - 1\) , \( a + 1\) , \( -20 a^{4} + 40 a^{3} + 93 a^{2} - 45 a - 38\) , \( 138 a^{4} - 229 a^{3} - 775 a^{2} + 167 a + 495\bigr] \) |
${y}^2+\left(2a^{4}-4a^{3}-9a^{2}+5a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+3a^{2}-8a-1\right){x}^{2}+\left(-20a^{4}+40a^{3}+93a^{2}-45a-38\right){x}+138a^{4}-229a^{3}-775a^{2}+167a+495$ |
| 99.1-a1 |
99.1-a |
$1$ |
$1$ |
5.5.173513.1 |
$5$ |
$[5, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( - 3^{6} \cdot 11 \) |
$58.93429$ |
$(a^3-2a^2-4a), (a^4-a^3-7a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.037285249$ |
$3492.550145$ |
4.68926695 |
\( \frac{1230619091}{297} a^{4} - \frac{1356468983}{297} a^{3} - \frac{7410172504}{297} a^{2} - \frac{2902148327}{297} a + \frac{1270596544}{297} \) |
\( \bigl[1\) , \( -2 a^{4} + 3 a^{3} + 11 a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 2 a\) , \( -7 a^{4} + 12 a^{3} + 34 a^{2} - a - 10\) , \( 2 a^{4} - 7 a^{3} - 4 a^{2} + 16 a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-2a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+11a^{2}-2\right){x}^{2}+\left(-7a^{4}+12a^{3}+34a^{2}-a-10\right){x}+2a^{4}-7a^{3}-4a^{2}+16a+5$ |
*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.
