| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$2$ |
$3$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$106.33821$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$5812.889473$ |
0.542748 |
\( -1574636278 a^{5} + 5316612558 a^{4} + 545822531 a^{3} - 14912259073 a^{2} + 11104951789 a - 1141781746 \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 9 a + 1\) , \( a^{5} - 5 a^{3} - a^{2} + 5 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -4 a^{5} + 12 a^{4} + 28 a^{3} - 44 a^{2} - 56 a + 12\) , \( -50 a^{5} + 70 a^{4} + 296 a^{3} - 255 a^{2} - 452 a + 132\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+9a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(a^{5}-5a^{3}-a^{2}+5a-1\right){x}^{2}+\left(-4a^{5}+12a^{4}+28a^{3}-44a^{2}-56a+12\right){x}-50a^{5}+70a^{4}+296a^{3}-255a^{2}-452a+132$ |
| 1.1-a2 |
1.1-a |
$2$ |
$3$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$106.33821$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$7.973785286$ |
0.542748 |
\( -112290975366347980766 a^{5} - 28653441342832557486 a^{4} + 496836451950423679683 a^{3} + 109832555815664447245 a^{2} - 426054601719310377175 a + 49792658574423095405 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a - 1\) , \( a^{2} + a - 1\) , \( -43 a^{5} + 72 a^{4} + 199 a^{3} - 220 a^{2} - 237 a + 6\) , \( -40 a^{5} - 230 a^{4} + 856 a^{3} + 731 a^{2} - 2190 a - 330\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a-1\right){x}^{2}+\left(-43a^{5}+72a^{4}+199a^{3}-220a^{2}-237a+6\right){x}-40a^{5}-230a^{4}+856a^{3}+731a^{2}-2190a-330$ |
| 5.1-a1 |
5.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$121.60092$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1522.280512$ |
1.27921 |
\( \frac{3399714969}{5} a^{5} - \frac{12546895642}{5} a^{4} + \frac{4212866592}{5} a^{3} + \frac{23475283529}{5} a^{2} - 3857680391 a + \frac{2010994454}{5} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 9 a + 5\) , \( a^{5} - 5 a^{3} - a^{2} + 5 a + 1\) , \( a^{4} + 2 a^{3} - 4 a^{2} - 4 a + 6\) , \( 3 a^{5} + a^{4} - 12 a^{3} - 5 a^{2} + 8 a + 1\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{5}-5a^{3}-a^{2}+5a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-9a+5\right){x}^{2}+\left(a^{4}+2a^{3}-4a^{2}-4a+6\right){x}+3a^{5}+a^{4}-12a^{3}-5a^{2}+8a+1$ |
| 5.1-a2 |
5.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5^{5} \) |
$121.60092$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1522.280512$ |
1.27921 |
\( -\frac{15790790179845246}{125} a^{5} + \frac{18408563487610828}{125} a^{4} + \frac{94310770717806452}{125} a^{3} - \frac{63441037940792326}{125} a^{2} - \frac{29533724112534309}{25} a + \frac{18928772029574064}{125} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 3\) , \( -a^{4} + a^{3} + 3 a^{2} - 3 a\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 6 a + 2\) , \( -3 a^{5} + 13 a^{4} - 6 a^{3} - 36 a^{2} + 37 a - 8\) , \( 23 a^{5} - 60 a^{4} - 35 a^{3} + 161 a^{2} - 99 a + 8\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+3\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+6a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-3a\right){x}^{2}+\left(-3a^{5}+13a^{4}-6a^{3}-36a^{2}+37a-8\right){x}+23a^{5}-60a^{4}-35a^{3}+161a^{2}-99a+8$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5^{11} \) |
$121.60092$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1635.770177$ |
1.37458 |
\( -\frac{2022517226}{15625} a^{5} - \frac{617784367}{15625} a^{4} + \frac{8872153252}{15625} a^{3} + \frac{2078657074}{15625} a^{2} - \frac{1524279067}{3125} a + \frac{882875824}{15625} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 7 a - 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 6 a^{2} + 11 a\) , \( a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 15 a - 3\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+7a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}^{2}+\left(a^{5}-2a^{4}-6a^{3}+6a^{2}+11a\right){x}+a^{5}-a^{4}-9a^{3}+5a^{2}+15a-3$ |
| 11.1-a1 |
11.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{5} \) |
$129.85901$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2735.194887$ |
2.29846 |
\( \frac{63593859758703}{161051} a^{5} - \frac{9129696300203}{161051} a^{4} - \frac{334923790397910}{161051} a^{3} - \frac{49424500135462}{161051} a^{2} + \frac{289836662471694}{161051} a - \frac{34253836421545}{161051} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 5 a + 3\) , \( a^{3} - 2 a + 1\) , \( -2 a^{5} - 4 a^{4} + 17 a^{3} + 8 a^{2} - 19 a + 7\) , \( -8 a^{5} + 33 a^{4} - 17 a^{3} - 65 a^{2} + 56 a - 3\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{5}-5a^{3}-3a^{2}+5a+3\right){x}^{2}+\left(-2a^{5}-4a^{4}+17a^{3}+8a^{2}-19a+7\right){x}-8a^{5}+33a^{4}-17a^{3}-65a^{2}+56a-3$ |
| 11.1-a2 |
11.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$129.85901$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2735.194887$ |
2.29846 |
\( \frac{24811}{11} a^{5} - \frac{39245}{11} a^{4} - \frac{153170}{11} a^{3} + \frac{198655}{11} a^{2} + \frac{245285}{11} a - \frac{237851}{11} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 4 a + 1\) , \( a^{2} + a - 2\) , \( a + 1\) , \( 4 a^{5} + 2 a^{4} - 18 a^{3} - 6 a^{2} + 17 a - 3\) , \( 10 a^{5} + 3 a^{4} - 45 a^{3} - 11 a^{2} + 40 a - 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(4a^{5}+2a^{4}-18a^{3}-6a^{2}+17a-3\right){x}+10a^{5}+3a^{4}-45a^{3}-11a^{2}+40a-5$ |
| 19.1-a1 |
19.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$135.91023$ |
$(a^3-4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$3373.786289$ |
2.83509 |
\( -\frac{76004209}{19} a^{5} - \frac{8116019}{19} a^{4} + \frac{320175202}{19} a^{3} + \frac{51876259}{19} a^{2} - 13757496 a + \frac{30746726}{19} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{5} - 6 a^{3} + 8 a - 2\) , \( -8 a^{4} + 11 a^{3} + 19 a^{2} - 26 a + 4\) , \( -7 a^{5} - 9 a^{4} + 40 a^{3} + 24 a^{2} - 46 a + 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a+1\right){x}{y}+\left(a^{5}-6a^{3}+8a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-8a^{4}+11a^{3}+19a^{2}-26a+4\right){x}-7a^{5}-9a^{4}+40a^{3}+24a^{2}-46a+5$ |
| 19.1-a2 |
19.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{5} \) |
$135.91023$ |
$(a^3-4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$3373.786289$ |
2.83509 |
\( -\frac{69743230731050}{2476099} a^{5} + \frac{25446217720951}{2476099} a^{4} + \frac{361633516576426}{2476099} a^{3} - \frac{6765366754937}{2476099} a^{2} - \frac{17345334081727}{130321} a + \frac{39929668562816}{2476099} \) |
\( \bigl[a^{2} - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - 2 a^{2} - 4 a\) , \( a^{5} - 6 a^{3} + 9 a - 2\) , \( 151 a^{5} - 299 a^{4} - 777 a^{3} + 1359 a^{2} + 1018 a - 1381\) , \( -4098 a^{5} + 7639 a^{4} + 21488 a^{3} - 33921 a^{2} - 28965 a + 32818\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{5}-6a^{3}+9a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-2a^{2}-4a\right){x}^{2}+\left(151a^{5}-299a^{4}-777a^{3}+1359a^{2}+1018a-1381\right){x}-4098a^{5}+7639a^{4}+21488a^{3}-33921a^{2}-28965a+32818$ |
| 19.3-a1 |
19.3-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
19.3 |
\( 19 \) |
\( -19 \) |
$135.91023$ |
$(a^4-a^3-4a^2+2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.026066778$ |
$21574.37911$ |
2.83548 |
\( -\frac{159578}{19} a^{5} + \frac{242328}{19} a^{4} + \frac{908716}{19} a^{3} - \frac{997883}{19} a^{2} - \frac{1359782}{19} a + \frac{759512}{19} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + a^{2} + 3 a + 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( 2 a^{5} - 2 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 4\) , \( 5 a^{5} - 2 a^{4} - 22 a^{3} + 6 a^{2} + 19 a - 8\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a+1\right){x}{y}+\left(a^{4}-5a^{2}-a+4\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+a^{2}+3a+1\right){x}^{2}+\left(2a^{5}-2a^{4}-7a^{3}+9a^{2}+4a-4\right){x}+5a^{5}-2a^{4}-22a^{3}+6a^{2}+19a-8$ |
| 19.3-a2 |
19.3-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{5} \) |
$135.91023$ |
$(a^4-a^3-4a^2+2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.005213355$ |
$21574.37911$ |
2.83548 |
\( -\frac{73060375014862}{2476099} a^{5} + \frac{137513496750823}{2476099} a^{4} + \frac{380940751081104}{2476099} a^{3} - \frac{610847394662201}{2476099} a^{2} - \frac{509896210790322}{2476099} a + \frac{592231979122059}{2476099} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{5} + 5 a^{3} + a^{2} - 4 a + 1\) , \( a^{2} + a - 2\) , \( 18 a^{5} - 38 a^{4} - 96 a^{3} + 172 a^{2} + 141 a - 158\) , \( -97 a^{5} + 167 a^{4} + 519 a^{3} - 722 a^{2} - 713 a + 662\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-4a+1\right){x}^{2}+\left(18a^{5}-38a^{4}-96a^{3}+172a^{2}+141a-158\right){x}-97a^{5}+167a^{4}+519a^{3}-722a^{2}-713a+662$ |
| 25.1-a1 |
25.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2388.631799$ |
2.00724 |
\( 1102536 a^{5} - 2070704 a^{4} - 5763268 a^{3} + 9215059 a^{2} + 7737141 a - 8964251 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{4} - 5 a^{2} + 5\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 4 a - 2\) , \( a^{5} + 2 a^{4} - 2 a^{3} - 6 a^{2} - 5 a - 3\) , \( 26 a^{5} - 25 a^{4} - 142 a^{3} + 93 a^{2} + 198 a - 56\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+4a-2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+5\right){x}^{2}+\left(a^{5}+2a^{4}-2a^{3}-6a^{2}-5a-3\right){x}+26a^{5}-25a^{4}-142a^{3}+93a^{2}+198a-56$ |
| 25.1-a2 |
25.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2388.631799$ |
2.00724 |
\( 2800825444556362378 a^{5} - 9461404002147808258 a^{4} - 965584023782643386 a^{3} + 26538078130827125782 a^{2} - 19766562305446365115 a + 2032415789521676968 \) |
\( \bigl[1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 7 a - 9\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 2\) , \( -6 a^{5} + 11 a^{4} + 23 a^{3} - 43 a^{2} - 21 a + 26\) , \( 14 a^{5} - 13 a^{4} - 57 a^{3} + 39 a^{2} + 35 a - 28\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+7a-9\right){x}^{2}+\left(-6a^{5}+11a^{4}+23a^{3}-43a^{2}-21a+26\right){x}+14a^{5}-13a^{4}-57a^{3}+39a^{2}+35a-28$ |
| 25.1-b1 |
25.1-b |
$2$ |
$3$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$2452.319989$ |
2.06075 |
\( -1574636278 a^{5} + 5316612558 a^{4} + 545822531 a^{3} - 14912259073 a^{2} + 11104951789 a - 1141781746 \) |
\( \bigl[a^{2} + a - 1\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 3\) , \( a^{3} - 3 a\) , \( 14 a^{4} + 4 a^{3} - 65 a^{2} - 26 a + 48\) , \( 164 a^{5} - 301 a^{4} - 850 a^{3} + 1351 a^{2} + 1135 a - 1326\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-3\right){x}^{2}+\left(14a^{4}+4a^{3}-65a^{2}-26a+48\right){x}+164a^{5}-301a^{4}-850a^{3}+1351a^{2}+1135a-1326$ |
| 25.1-b2 |
25.1-b |
$2$ |
$3$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$272.4799988$ |
2.06075 |
\( -112290975366347980766 a^{5} - 28653441342832557486 a^{4} + 496836451950423679683 a^{3} + 109832555815664447245 a^{2} - 426054601719310377175 a + 49792658574423095405 \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 9 a + 1\) , \( a^{5} - 5 a^{3} - a^{2} + 4 a\) , \( a^{4} - 5 a^{2} + 5\) , \( -168 a^{5} + 603 a^{4} - 40 a^{3} - 1626 a^{2} + 1463 a - 327\) , \( -6233 a^{5} + 19124 a^{4} + 8423 a^{3} - 57535 a^{2} + 25889 a + 6622\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+9a+1\right){x}{y}+\left(a^{4}-5a^{2}+5\right){y}={x}^{3}+\left(a^{5}-5a^{3}-a^{2}+4a\right){x}^{2}+\left(-168a^{5}+603a^{4}-40a^{3}-1626a^{2}+1463a-327\right){x}-6233a^{5}+19124a^{4}+8423a^{3}-57535a^{2}+25889a+6622$ |
| 25.1-c1 |
25.1-c |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$23054.05111$ |
1.54984 |
\( \frac{3399714969}{5} a^{5} - \frac{12546895642}{5} a^{4} + \frac{4212866592}{5} a^{3} + \frac{23475283529}{5} a^{2} - 3857680391 a + \frac{2010994454}{5} \) |
\( \bigl[a^{5} - 5 a^{3} - 2 a^{2} + 6 a + 3\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 8 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -2 a^{5} + 6 a^{4} + 12 a^{3} - 26 a^{2} - 17 a + 27\) , \( -7 a^{5} + 17 a^{4} + 43 a^{3} - 68 a^{2} - 73 a + 43\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-2a^{2}+6a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a^{5}-6a^{3}-2a^{2}+8a+1\right){x}^{2}+\left(-2a^{5}+6a^{4}+12a^{3}-26a^{2}-17a+27\right){x}-7a^{5}+17a^{4}+43a^{3}-68a^{2}-73a+43$ |
| 25.1-c2 |
25.1-c |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{11} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$36.88648177$ |
1.54984 |
\( -\frac{15790790179845246}{125} a^{5} + \frac{18408563487610828}{125} a^{4} + \frac{94310770717806452}{125} a^{3} - \frac{63441037940792326}{125} a^{2} - \frac{29533724112534309}{25} a + \frac{18928772029574064}{125} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{5} - 6 a^{3} + 9 a - 1\) , \( -43 a^{5} + 154 a^{4} - 41 a^{3} - 300 a^{2} + 237 a - 24\) , \( -1645 a^{5} + 6061 a^{4} - 2006 a^{3} - 11386 a^{2} + 9335 a - 973\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}+9a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-43a^{5}+154a^{4}-41a^{3}-300a^{2}+237a-24\right){x}-1645a^{5}+6061a^{4}-2006a^{3}-11386a^{2}+9335a-973$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$2202.388689$ |
1.85073 |
\( -167867068 a^{5} + 566951849 a^{4} + 58167307 a^{3} - 1590270105 a^{2} + 1183849460 a - 121716255 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 4 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 5 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 7 a - 2\) , \( 19 a^{5} - 12 a^{4} - 86 a^{3} + 53 a^{2} + 85 a - 66\) , \( 7 a^{5} + 65 a^{4} - 6 a^{3} - 285 a^{2} - 71 a + 226\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+4a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+7a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+5a-2\right){x}^{2}+\left(19a^{5}-12a^{4}-86a^{3}+53a^{2}+85a-66\right){x}+7a^{5}+65a^{4}-6a^{3}-285a^{2}-71a+226$ |
| 25.1-e1 |
25.1-e |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 3 \) |
$0.128793408$ |
$43779.36927$ |
3.41150 |
\( 1102536 a^{5} - 2070704 a^{4} - 5763268 a^{3} + 9215059 a^{2} + 7737141 a - 8964251 \) |
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{5} + a^{4} + 4 a^{3} - a^{2} - 2 a - 2\) , \( a^{3} - 2 a\) , \( -3 a^{5} + 26 a^{4} - 15 a^{3} - 72 a^{2} + 67 a - 7\) , \( -3 a^{5} + 64 a^{4} - 57 a^{3} - 182 a^{2} + 178 a - 19\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-a^{2}-2a-2\right){x}^{2}+\left(-3a^{5}+26a^{4}-15a^{3}-72a^{2}+67a-7\right){x}-3a^{5}+64a^{4}-57a^{3}-182a^{2}+178a-19$ |
| 25.1-e2 |
25.1-e |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{8} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.4[2] |
$25$ |
\( 3 \) |
$0.643967044$ |
$14.00939816$ |
3.41150 |
\( 2800825444556362378 a^{5} - 9461404002147808258 a^{4} - 965584023782643386 a^{3} + 26538078130827125782 a^{2} - 19766562305446365115 a + 2032415789521676968 \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 5\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( -23 a^{5} + 82 a^{4} + 9 a^{3} - 243 a^{2} + 152 a + 5\) , \( -123 a^{5} + 480 a^{4} - 66 a^{3} - 1360 a^{2} + 1131 a - 142\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-a-5\right){x}^{2}+\left(-23a^{5}+82a^{4}+9a^{3}-243a^{2}+152a+5\right){x}-123a^{5}+480a^{4}-66a^{3}-1360a^{2}+1131a-142$ |
| 25.1-f1 |
25.1-f |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.006055981$ |
$33575.54655$ |
3.07560 |
\( -167867068 a^{5} + 566951849 a^{4} + 58167307 a^{3} - 1590270105 a^{2} + 1183849460 a - 121716255 \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a\) , \( a^{5} - 6 a^{3} + 9 a - 2\) , \( -3 a^{5} - 2 a^{4} + 20 a^{3} + 7 a^{2} - 32 a - 4\) , \( -3 a^{5} - 6 a^{4} + 8 a^{3} + 26 a^{2} + 7 a - 17\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a+1\right){x}{y}+\left(a^{5}-6a^{3}+9a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a\right){x}^{2}+\left(-3a^{5}-2a^{4}+20a^{3}+7a^{2}-32a-4\right){x}-3a^{5}-6a^{4}+8a^{3}+26a^{2}+7a-17$ |
| 25.1-g1 |
25.1-g |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{17} \) |
$139.05428$ |
$(-a^5+a^4+6a^3-4a^2-9a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$889.4761405$ |
1.49491 |
\( -\frac{2022517226}{15625} a^{5} - \frac{617784367}{15625} a^{4} + \frac{8872153252}{15625} a^{3} + \frac{2078657074}{15625} a^{2} - \frac{1524279067}{3125} a + \frac{882875824}{15625} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 4 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a - 1\) , \( a^{5} - 6 a^{3} + 9 a - 2\) , \( 3 a^{5} + 17 a^{4} - 30 a^{3} - 54 a^{2} + 61 a - 7\) , \( 8 a^{5} + 55 a^{4} - 92 a^{3} - 168 a^{2} + 192 a - 21\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+4a-1\right){x}{y}+\left(a^{5}-6a^{3}+9a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a-1\right){x}^{2}+\left(3a^{5}+17a^{4}-30a^{3}-54a^{2}+61a-7\right){x}+8a^{5}+55a^{4}-92a^{3}-168a^{2}+192a-21$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$139.05428$ |
$(-a^4-a^3+4a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.046922409$ |
$7045.596578$ |
3.33372 |
\( -\frac{43744841876}{5} a^{5} + 1265583542 a^{4} + 46083941204 a^{3} + \frac{33773457692}{5} a^{2} - \frac{199596724451}{5} a + \frac{23593369576}{5} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 7 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 3\) , \( a^{5} - 6 a^{3} + 8 a - 1\) , \( -16 a^{5} + 21 a^{4} + 89 a^{3} - 69 a^{2} - 131 a + 14\) , \( -67 a^{5} + 86 a^{4} + 379 a^{3} - 289 a^{2} - 561 a + 81\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+7a-4\right){x}{y}+\left(a^{5}-6a^{3}+8a-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a-3\right){x}^{2}+\left(-16a^{5}+21a^{4}+89a^{3}-69a^{2}-131a+14\right){x}-67a^{5}+86a^{4}+379a^{3}-289a^{2}-561a+81$ |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{20} \) |
$139.05428$ |
$(-a^4-a^3+4a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.037494794$ |
$7998.934301$ |
3.78045 |
\( \frac{4894818556073153}{3125} a^{5} + \frac{1249017651449822}{3125} a^{4} - \frac{4331468777462849}{625} a^{3} - \frac{4787655279108426}{3125} a^{2} + \frac{18571928058850341}{3125} a - \frac{2170486277732452}{3125} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 4 a - 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 1\) , \( a^{3} - 2 a + 1\) , \( 32 a^{5} - 76 a^{4} - 58 a^{3} + 221 a^{2} - 97 a - 17\) , \( 218 a^{5} - 658 a^{4} - 156 a^{3} + 1832 a^{2} - 1331 a + 161\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+4a-1\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a-1\right){x}^{2}+\left(32a^{5}-76a^{4}-58a^{3}+221a^{2}-97a-17\right){x}+218a^{5}-658a^{4}-156a^{3}+1832a^{2}-1331a+161$ |
| 25.2-b2 |
25.2-b |
$2$ |
$2$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$139.05428$ |
$(-a^4-a^3+4a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.018747397$ |
$31995.73720$ |
3.78045 |
\( \frac{33720021}{125} a^{5} + \frac{19059678}{125} a^{4} - \frac{153948129}{125} a^{3} - \frac{67251051}{125} a^{2} + \frac{130688077}{125} a + \frac{4302972}{125} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 7 a - 1\) , \( -a^{5} + 6 a^{3} + a^{2} - 9 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -16 a^{5} - 4 a^{4} + 74 a^{3} + 16 a^{2} - 70 a + 8\) , \( 73 a^{5} + 18 a^{4} - 322 a^{3} - 68 a^{2} + 275 a - 35\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+7a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-9a+1\right){x}^{2}+\left(-16a^{5}-4a^{4}+74a^{3}+16a^{2}-70a+8\right){x}+73a^{5}+18a^{4}-322a^{3}-68a^{2}+275a-35$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$140.78483$ |
$(a^3-4a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2547.634678$ |
2.14085 |
\( -\frac{2973625998}{29} a^{5} - \frac{851634307}{29} a^{4} + \frac{13289092493}{29} a^{3} + \frac{3095200361}{29} a^{2} - \frac{11503056457}{29} a + \frac{1340891512}{29} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 6 a^{2} + a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 4 a^{5} - 2 a^{4} - 20 a^{3} + 4 a^{2} + 18 a - 6\) , \( 5 a^{5} - a^{4} - 26 a^{3} - 2 a^{2} + 23 a - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+6a^{2}+a-3\right){x}^{2}+\left(4a^{5}-2a^{4}-20a^{3}+4a^{2}+18a-6\right){x}+5a^{5}-a^{4}-26a^{3}-2a^{2}+23a-4$ |
| 29.1-b1 |
29.1-b |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{5} \) |
$140.78483$ |
$(a^3-4a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2084.065013$ |
1.75130 |
\( \frac{40479508478927910}{20511149} a^{5} - \frac{15024435861926757}{20511149} a^{4} - \frac{212969184677615002}{20511149} a^{3} + \frac{17029578879037578}{20511149} a^{2} + \frac{197549662155120709}{20511149} a - \frac{62089086789284103}{20511149} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 8 a^{2} - 8 a + 7\) , \( a^{3} - 3 a + 1\) , \( 7 a^{5} - 26 a^{4} + 11 a^{3} + 46 a^{2} - 47 a + 12\) , \( -23 a^{5} + 89 a^{4} - 33 a^{3} - 169 a^{2} + 137 a - 12\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-8a^{2}-8a+7\right){x}^{2}+\left(7a^{5}-26a^{4}+11a^{3}+46a^{2}-47a+12\right){x}-23a^{5}+89a^{4}-33a^{3}-169a^{2}+137a-12$ |
| 29.1-b2 |
29.1-b |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$140.78483$ |
$(a^3-4a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2084.065013$ |
1.75130 |
\( -\frac{4165233051}{29} a^{5} + \frac{13376042750}{29} a^{4} + \frac{3201090228}{29} a^{3} - \frac{37752457624}{29} a^{2} + \frac{24249404186}{29} a - \frac{2418974392}{29} \) |
\( \bigl[a^{4} - 5 a^{2} + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( -5 a^{5} + 7 a^{4} + 23 a^{3} - 26 a^{2} - 26 a + 24\) , \( -2 a^{5} + 4 a^{4} + 8 a^{3} - 16 a^{2} - 10 a + 13\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+5\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a\right){x}^{2}+\left(-5a^{5}+7a^{4}+23a^{3}-26a^{2}-26a+24\right){x}-2a^{5}+4a^{4}+8a^{3}-16a^{2}-10a+13$ |
| 49.1-a1 |
49.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{4} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$40619.12334$ |
2.73067 |
\( -\frac{936417}{49} a^{5} - \frac{2863568}{7} a^{4} + \frac{4700774}{7} a^{3} + \frac{40491841}{49} a^{2} - \frac{51661791}{49} a + \frac{5689126}{49} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 4 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 10 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 1\) , \( -2 a^{5} + 6 a^{4} + 13 a^{3} - 22 a^{2} - 25 a + 11\) , \( -3 a^{5} + 10 a^{4} + 19 a^{3} - 41 a^{2} - 34 a + 30\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+4a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-10a+1\right){x}^{2}+\left(-2a^{5}+6a^{4}+13a^{3}-22a^{2}-25a+11\right){x}-3a^{5}+10a^{4}+19a^{3}-41a^{2}-34a+30$ |
| 49.1-a2 |
49.1-a |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{20} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$625$ |
\( 2 \) |
$1$ |
$2.599623893$ |
2.73067 |
\( -\frac{3215348619198652801962500}{5764801} a^{5} + \frac{183670830123977364687583130}{282475249} a^{4} + \frac{940982567218403648250175996}{282475249} a^{3} - \frac{632980851785016406997877764}{282475249} a^{2} - \frac{1473358730028708471470341123}{282475249} a + \frac{188861210398380073025703508}{282475249} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 4 a + 3\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 6 a + 3\) , \( 53 a^{5} - 54 a^{4} - 396 a^{3} + 410 a^{2} + 602 a - 556\) , \( 695 a^{5} - 1325 a^{4} - 3373 a^{3} + 5478 a^{2} + 4339 a - 5128\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+6a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-4a+3\right){x}^{2}+\left(53a^{5}-54a^{4}-396a^{3}+410a^{2}+602a-556\right){x}+695a^{5}-1325a^{4}-3373a^{3}+5478a^{2}+4339a-5128$ |
| 49.1-b1 |
49.1-b |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{10} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.017406501$ |
$8181.661056$ |
3.59024 |
\( -\frac{4939187349}{2401} a^{5} + \frac{173504057023}{16807} a^{4} - \frac{119924637876}{16807} a^{3} - \frac{361352161599}{16807} a^{2} + \frac{345673197517}{16807} a - \frac{37325508713}{16807} \) |
\( \bigl[a^{5} - 5 a^{3} - a^{2} + 6 a\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 5 a^{2} - 2 a + 1\) , \( 1\) , \( 3 a^{5} + 19 a^{4} - 24 a^{3} - 81 a^{2} + 82 a - 9\) , \( 74 a^{5} - 133 a^{4} - 184 a^{3} + 441 a^{2} - 224 a + 21\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-a^{2}+6a\right){x}{y}+{y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-5a^{2}-2a+1\right){x}^{2}+\left(3a^{5}+19a^{4}-24a^{3}-81a^{2}+82a-9\right){x}+74a^{5}-133a^{4}-184a^{3}+441a^{2}-224a+21$ |
| 49.1-b2 |
49.1-b |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.087032508$ |
$8181.661056$ |
3.59024 |
\( -\frac{2123565121}{7} a^{5} + 353664403 a^{4} + 1811834506 a^{3} - \frac{8531638866}{7} a^{2} - \frac{19858243964}{7} a + \frac{2545514855}{7} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 4 a + 1\) , \( a^{3} - 4 a\) , \( a^{4} - 5 a^{2} - a + 5\) , \( 4 a^{5} - 4 a^{4} - 12 a^{3} + 11 a^{2} + 2 a - 4\) , \( 7 a^{5} - 8 a^{4} - 21 a^{3} + 19 a^{2} + 8 a - 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+4a+1\right){x}{y}+\left(a^{4}-5a^{2}-a+5\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(4a^{5}-4a^{4}-12a^{3}+11a^{2}+2a-4\right){x}+7a^{5}-8a^{4}-21a^{3}+19a^{2}+8a-7$ |
| 49.1-c1 |
49.1-c |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 1 \) |
$1$ |
$374.5596643$ |
3.17799 |
\( \frac{11257601323029}{7} a^{5} - \frac{23570834837528}{7} a^{4} - \frac{56341604918436}{7} a^{3} + \frac{108961940404038}{7} a^{2} + \frac{71138545732615}{7} a - \frac{115384993083988}{7} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 2\) , \( -a^{3} + 4 a + 1\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 6 a + 2\) , \( -a^{5} + 5 a^{4} + 5 a^{3} - 42 a^{2} + 36 a - 2\) , \( -210 a^{5} + 699 a^{4} + 54 a^{3} - 1852 a^{2} + 1376 a - 144\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-2\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+6a+2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-a^{5}+5a^{4}+5a^{3}-42a^{2}+36a-2\right){x}-210a^{5}+699a^{4}+54a^{3}-1852a^{2}+1376a-144$ |
| 49.1-d1 |
49.1-d |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.015652884$ |
$52853.08760$ |
4.17124 |
\( -\frac{44671}{7} a^{5} + \frac{164659}{7} a^{4} - \frac{51517}{7} a^{3} - 44469 a^{2} + \frac{245915}{7} a - \frac{21811}{7} \) |
\( \bigl[a^{5} - 5 a^{3} - 2 a^{2} + 6 a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 6\) , \( a^{5} - 6 a^{3} + 8 a - 2\) , \( 2 a^{5} + 7 a^{4} - 8 a^{3} - 32 a^{2} + 2 a + 27\) , \( 3 a^{5} + 17 a^{4} - 9 a^{3} - 75 a^{2} - 8 a + 60\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-2a^{2}+6a+3\right){x}{y}+\left(a^{5}-6a^{3}+8a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+9a-6\right){x}^{2}+\left(2a^{5}+7a^{4}-8a^{3}-32a^{2}+2a+27\right){x}+3a^{5}+17a^{4}-9a^{3}-75a^{2}-8a+60$ |
| 49.1-e1 |
49.1-e |
$1$ |
$1$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{4} \) |
$147.07506$ |
$(a^4-4a^2+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$433.1924947$ |
0.728048 |
\( -\frac{1421117311}{49} a^{5} + \frac{4782332379}{49} a^{4} + \frac{513865427}{49} a^{3} - \frac{13401689351}{49} a^{2} + \frac{9976777114}{49} a - \frac{1036539037}{49} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{4} - 4 a^{2} + 1\) , \( a^{3} - 3 a + 1\) , \( 9 a^{5} + 2 a^{4} - 43 a^{3} - 5 a^{2} + 43 a - 11\) , \( 25 a^{5} + 2 a^{4} - 108 a^{3} - 11 a^{2} + 93 a - 19\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+1\right){x}^{2}+\left(9a^{5}+2a^{4}-43a^{3}-5a^{2}+43a-11\right){x}+25a^{5}+2a^{4}-108a^{3}-11a^{2}+93a-19$ |
| 55.1-a1 |
55.1-a |
$4$ |
$10$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1395.429054$ |
1.17262 |
\( -\frac{289878866696566585}{121} a^{5} + \frac{5349044586996476976}{605} a^{4} - \frac{1795968845688972074}{605} a^{3} - \frac{10008068540204885393}{605} a^{2} + \frac{8223038630475819114}{605} a - \frac{857323320582179609}{605} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 4 a - 1\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 9 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( -95 a^{5} - 23 a^{4} + 424 a^{3} + 90 a^{2} - 372 a + 42\) , \( -395 a^{5} - 101 a^{4} + 1745 a^{3} + 389 a^{2} - 1490 a + 170\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+4a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-1\right){y}={x}^{3}+\left(a^{5}-6a^{3}-2a^{2}+9a+1\right){x}^{2}+\left(-95a^{5}-23a^{4}+424a^{3}+90a^{2}-372a+42\right){x}-395a^{5}-101a^{4}+1745a^{3}+389a^{2}-1490a+170$ |
| 55.1-a2 |
55.1-a |
$4$ |
$10$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{10} \cdot 11^{10} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1395.429054$ |
1.17262 |
\( \frac{1943022822726752256641376554}{81054451878125} a^{5} + \frac{495803751615222489785708994}{81054451878125} a^{4} - \frac{8596991577817299223627112832}{81054451878125} a^{3} - \frac{1900483535098948610165690039}{81054451878125} a^{2} + \frac{7372220493083145853425765754}{81054451878125} a - \frac{172317096216800925132626832}{16210890375625} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 8 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 2\) , \( -41 a^{5} + 46 a^{4} + 240 a^{3} - 152 a^{2} - 367 a + 34\) , \( -411 a^{5} + 568 a^{4} + 2368 a^{3} - 2199 a^{2} - 3570 a + 1375\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-2a^{2}+8a+1\right){x}^{2}+\left(-41a^{5}+46a^{4}+240a^{3}-152a^{2}-367a+34\right){x}-411a^{5}+568a^{4}+2368a^{3}-2199a^{2}-3570a+1375$ |
| 55.1-a3 |
55.1-a |
$4$ |
$10$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$5581.716218$ |
1.17262 |
\( \frac{318810067}{55} a^{5} - \frac{1694594966}{55} a^{4} + \frac{2224927206}{55} a^{3} + \frac{1817891772}{55} a^{2} - \frac{1078722042}{11} a + \frac{2634551562}{55} \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 2 a^{2} - 5 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 2\) , \( 3 a^{5} + 2 a^{4} - 11 a^{3} - 8 a^{2} + 6 a + 3\) , \( 15 a^{5} - 70 a^{3} - a^{2} + 71 a - 9\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-2a^{2}-5a-1\right){x}^{2}+\left(3a^{5}+2a^{4}-11a^{3}-8a^{2}+6a+3\right){x}+15a^{5}-70a^{3}-a^{2}+71a-9$ |
| 55.1-a4 |
55.1-a |
$4$ |
$10$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{5} \cdot 11^{5} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$5581.716218$ |
1.17262 |
\( \frac{2540935961496772}{20131375} a^{5} - \frac{8702003324009521}{20131375} a^{4} - \frac{729306987638464}{20131375} a^{3} + \frac{24425243774243932}{20131375} a^{2} - \frac{3661635311508572}{4026275} a + \frac{1886187686106652}{20131375} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 8 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 2\) , \( 9 a^{5} - 19 a^{4} - 50 a^{3} + 93 a^{2} + 73 a - 101\) , \( -40 a^{5} + 69 a^{4} + 220 a^{3} - 306 a^{2} - 314 a + 289\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-2a^{2}+8a+1\right){x}^{2}+\left(9a^{5}-19a^{4}-50a^{3}+93a^{2}+73a-101\right){x}-40a^{5}+69a^{4}+220a^{3}-306a^{2}-314a+289$ |
| 55.1-b1 |
55.1-b |
$2$ |
$3$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{9} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1.177560022$ |
$9.049130389$ |
4.35187 |
\( -\frac{662630359696904314656}{11789738455} a^{5} + \frac{2459277588205067303253}{11789738455} a^{4} - \frac{876029171610430507488}{11789738455} a^{3} - \frac{4556982804515100977771}{11789738455} a^{2} + \frac{773673341790400476549}{2357947691} a - \frac{470510104426284789121}{11789738455} \) |
\( \bigl[a^{5} - 5 a^{3} - a^{2} + 6 a\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 8 a - 2\) , \( a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( 36 a^{5} - 126 a^{4} + 40 a^{3} + 225 a^{2} - 179 a + 17\) , \( 413 a^{5} - 1527 a^{4} + 529 a^{3} + 2821 a^{2} - 2330 a + 242\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-a^{2}+6a\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+3a^{2}+8a-2\right){x}^{2}+\left(36a^{5}-126a^{4}+40a^{3}+225a^{2}-179a+17\right){x}+413a^{5}-1527a^{4}+529a^{3}+2821a^{2}-2330a+242$ |
| 55.1-b2 |
55.1-b |
$2$ |
$3$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.392520007$ |
$6596.816053$ |
4.35187 |
\( \frac{346117819}{33275} a^{5} + \frac{3582553}{33275} a^{4} - \frac{1940323608}{33275} a^{3} - \frac{352709871}{33275} a^{2} + \frac{354581352}{6655} a - \frac{246487801}{33275} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 7 a - 4\) , \( a^{5} - 2 a^{4} - a^{3} + 5 a^{2} - 5 a + 2\) , \( a^{5} + 3 a^{4} - 8 a^{3} - 8 a^{2} + 14 a - 4\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+7a-4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(a^{5}-2a^{4}-a^{3}+5a^{2}-5a+2\right){x}+a^{5}+3a^{4}-8a^{3}-8a^{2}+14a-4$ |
| 55.1-c1 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{36} \cdot 11 \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$324$ |
\( 2 \) |
$4.478385603$ |
$0.984898323$ |
3.60270 |
\( -\frac{68860445600253667049494865623597}{41961669921875} a^{5} + \frac{50826893655747855586256847043844}{8392333984375} a^{4} - \frac{85330518229794645405920125041787}{41961669921875} a^{3} - \frac{475486585422138548160288303307589}{41961669921875} a^{2} + \frac{390681876487061411010300890829621}{41961669921875} a - \frac{40732027471892286337032079089888}{41961669921875} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 5 a^{2} - 9 a + 7\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( 112 a^{5} - 922 a^{4} + 775 a^{3} + 1693 a^{2} - 1593 a + 78\) , \( 4164 a^{5} - 29492 a^{4} + 23784 a^{3} + 57735 a^{2} - 56003 a + 5371\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-5a^{2}-9a+7\right){x}^{2}+\left(112a^{5}-922a^{4}+775a^{3}+1693a^{2}-1593a+78\right){x}+4164a^{5}-29492a^{4}+23784a^{3}+57735a^{2}-56003a+5371$ |
| 55.1-c2 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.373198800$ |
$22975.70809$ |
3.60270 |
\( -\frac{11235672312}{33275} a^{5} + \frac{20982418976}{33275} a^{4} + \frac{59004947679}{33275} a^{3} - \frac{93643005727}{33275} a^{2} - \frac{3183918349}{1331} a + \frac{91652565493}{33275} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{4} - 2 a^{3} - a^{2} + 2 a\) , \( a^{5} - 2 a^{4} - a^{3} + 3 a^{2} - a\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}^{2}+\left(a^{4}-2a^{3}-a^{2}+2a\right){x}+a^{5}-2a^{4}-a^{3}+3a^{2}-a$ |
| 55.1-c3 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.746397600$ |
$11487.85404$ |
3.60270 |
\( \frac{5330731523591132}{221445125} a^{5} - \frac{743963416430104}{8857805} a^{4} - \frac{1201591749019133}{221445125} a^{3} + \frac{52611252383091049}{221445125} a^{2} - \frac{38685468531902921}{221445125} a + \frac{3966791168946448}{221445125} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 5 a^{2} - 9 a + 7\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( -8 a^{5} + 8 a^{4} + 30 a^{3} - 27 a^{2} - 18 a + 13\) , \( 15 a^{5} - 4 a^{4} - 58 a^{3} + 4 a^{2} + 33 a - 1\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-5a^{2}-9a+7\right){x}^{2}+\left(-8a^{5}+8a^{4}+30a^{3}-27a^{2}-18a+13\right){x}+15a^{5}-4a^{4}-58a^{3}+4a^{2}+33a-1$ |
| 55.1-c4 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{12} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.492795201$ |
$1435.981755$ |
3.60270 |
\( -\frac{1134772419910409565690056008}{78460709418025} a^{5} + \frac{168526375549103303908764734}{78460709418025} a^{4} + \frac{5988114100787529589686607761}{78460709418025} a^{3} + \frac{878677619371933888671459807}{78460709418025} a^{2} - \frac{207315883439060288004824035}{3138428376721} a + \frac{612609901060209365342912687}{78460709418025} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( 95 a^{5} - 54 a^{4} - 437 a^{3} + 4 a^{2} + 322 a - 40\) , \( 879 a^{5} + 152 a^{4} - 5105 a^{3} - 1271 a^{2} + 4769 a - 557\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}^{2}+\left(95a^{5}-54a^{4}-437a^{3}+4a^{2}+322a-40\right){x}+879a^{5}+152a^{4}-5105a^{3}-1271a^{2}+4769a-557$ |
| 55.1-c5 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{3} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1.492795201$ |
$717.9908779$ |
3.60270 |
\( \frac{31012401516055249547384}{4159375} a^{5} - \frac{523718407451866991609626}{20796875} a^{4} - \frac{53694158037740945689731}{20796875} a^{3} + \frac{1468997348651898608895283}{20796875} a^{2} - \frac{1093645797638147761408399}{20796875} a + \frac{112439678672230837789619}{20796875} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 5 a^{2} - 9 a + 7\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( -43 a^{5} + 113 a^{4} + 75 a^{3} - 337 a^{2} + 152 a + 3\) , \( 262 a^{5} - 848 a^{4} - 135 a^{3} + 2333 a^{2} - 1658 a + 182\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-5a^{2}-9a+7\right){x}^{2}+\left(-43a^{5}+113a^{4}+75a^{3}-337a^{2}+152a+3\right){x}+262a^{5}-848a^{4}-135a^{3}+2333a^{2}-1658a+182$ |
| 55.1-c6 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{9} \cdot 11 \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1.119596400$ |
$31.51674635$ |
3.60270 |
\( -\frac{68122406991656148506438}{34375} a^{5} + \frac{127872188190915482669604}{34375} a^{4} + \frac{356328243428418724069901}{34375} a^{3} - \frac{569306923809174095949038}{34375} a^{2} - \frac{95741090533229568010646}{6875} a + \frac{554266079267540841273337}{34375} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( 40 a^{5} - 34 a^{4} - 167 a^{3} + 44 a^{2} + 122 a - 30\) , \( 180 a^{5} - 110 a^{4} - 802 a^{3} + 59 a^{2} + 602 a - 98\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}^{2}+\left(40a^{5}-34a^{4}-167a^{3}+44a^{2}+122a-30\right){x}+180a^{5}-110a^{4}-802a^{3}+59a^{2}+602a-98$ |
| 55.1-c7 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{18} \cdot 11^{2} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$81$ |
\( 2^{2} \) |
$2.239192801$ |
$15.75837317$ |
3.60270 |
\( -\frac{37689081725029512896836815827}{236328125} a^{5} + \frac{5413998512197933096193974657}{236328125} a^{4} + \frac{39699138046370103416731775129}{47265625} a^{3} + \frac{5855187916019500691170117907}{47265625} a^{2} - \frac{171788070329117798611584024321}{236328125} a + \frac{20302777608923852244134294324}{236328125} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 4 a\) , \( a^{4} - a^{3} - 5 a^{2} + a + 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 22 a^{5} - 172 a^{4} - 57 a^{3} + 891 a^{2} - 55 a - 1195\) , \( 1173 a^{5} - 3539 a^{4} - 5592 a^{3} + 16888 a^{2} + 6600 a - 19018\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+4a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+5\right){x}^{2}+\left(22a^{5}-172a^{4}-57a^{3}+891a^{2}-55a-1195\right){x}+1173a^{5}-3539a^{4}-5592a^{3}+16888a^{2}+6600a-19018$ |
| 55.1-c8 |
55.1-c |
$8$ |
$12$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{9} \cdot 11^{4} \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2^{2} \) |
$4.478385603$ |
$1.969796647$ |
3.60270 |
\( -\frac{9433303546579626471768072180865059296032553215397}{45753125} a^{5} + \frac{1355084523804655378375453566788451852023805657076}{45753125} a^{4} + \frac{49682030257732800965290263075092647855395797374269}{45753125} a^{3} + \frac{7327555144507472390843666427103957839244353235203}{45753125} a^{2} - \frac{8599461376758185884778299818810506961700814415799}{9150625} a + \frac{5081637844423682255349943480551045188994976385328}{45753125} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 5 a^{2} - 9 a + 7\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 3\) , \( 1092 a^{5} - 292 a^{4} - 5635 a^{3} - 517 a^{2} + 4707 a - 652\) , \( 43794 a^{5} - 6594 a^{4} - 229060 a^{3} - 32395 a^{2} + 197587 a - 23967\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-5a^{2}-9a+7\right){x}^{2}+\left(1092a^{5}-292a^{4}-5635a^{3}-517a^{2}+4707a-652\right){x}+43794a^{5}-6594a^{4}-229060a^{3}-32395a^{2}+197587a-23967$ |
| 55.1-d1 |
55.1-d |
$2$ |
$5$ |
6.6.1416125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$148.49765$ |
$(-a^5+a^4+6a^3-4a^2-9a+4), (-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1626.578459$ |
1.36686 |
\( -\frac{218418915702741}{55} a^{5} + \frac{737606565017638}{55} a^{4} + \frac{75883309677192}{55} a^{3} - \frac{2068973489267746}{55} a^{2} + \frac{307953968457281}{11} a - \frac{158295936753121}{55} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a - 1\) , \( a^{5} - 7 a^{3} + 10 a - 3\) , \( a^{5} - 6 a^{3} - a^{2} + 9 a + 1\) , \( -50 a^{5} + 159 a^{4} + 33 a^{3} - 445 a^{2} + 313 a - 30\) , \( -384 a^{5} + 1302 a^{4} + 126 a^{3} - 3654 a^{2} + 2724 a - 282\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a-1\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+9a+1\right){y}={x}^{3}+\left(a^{5}-7a^{3}+10a-3\right){x}^{2}+\left(-50a^{5}+159a^{4}+33a^{3}-445a^{2}+313a-30\right){x}-384a^{5}+1302a^{4}+126a^{3}-3654a^{2}+2724a-282$ |
*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.
