| 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 |
$4$ |
$39$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$58.90795$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 13$ |
3B, 13B.1.2 |
$28561$ |
\( 1 \) |
$1$ |
$0.014802157$ |
0.641303 |
\( 14273264587780952609125805373809022 a^{5} - 33978664183724880412077066535252082 a^{4} - 44161420314998729136586656312921749 a^{3} + 88173325697661842578861191186611639 a^{2} + 23535955393860563533538162020788064 a - 37503869415369575938251635322944654 \) |
\( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -2015 a^{5} + 2317 a^{4} + 10491 a^{3} - 2078 a^{2} - 11628 a - 4340\) , \( -87669 a^{5} + 112368 a^{4} + 435832 a^{3} - 134018 a^{2} - 464939 a - 144427\bigr] \) |
${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-3\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}^{2}+\left(-2015a^{5}+2317a^{4}+10491a^{3}-2078a^{2}-11628a-4340\right){x}-87669a^{5}+112368a^{4}+435832a^{3}-134018a^{2}-464939a-144427$ |
| 1.1-a2 |
1.1-a |
$4$ |
$39$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$58.90795$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 13$ |
3B, 13B.1.2 |
$28561$ |
\( 1 \) |
$1$ |
$0.014802157$ |
0.641303 |
\( -299441694155033880148130654153024 a^{5} - 187917845986491657242090310571049 a^{4} + 704001225414123443403572247320027 a^{3} + 352597497846354900118604631201756 a^{2} - 271295440361411180696560081353475 a - 113961855027594415883614627224113 \) |
\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 2 a - 3\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a\) , \( 670 a^{5} - 2194 a^{4} + 16 a^{3} + 3065 a^{2} - 90 a - 1279\) , \( 20194 a^{5} - 68427 a^{4} + 14638 a^{3} + 73555 a^{2} - 10467 a - 21619\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+a-1\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-4a^{4}+11a^{2}-2a-3\right){x}^{2}+\left(670a^{5}-2194a^{4}+16a^{3}+3065a^{2}-90a-1279\right){x}+20194a^{5}-68427a^{4}+14638a^{3}+73555a^{2}-10467a-21619$ |
| 1.1-a3 |
1.1-a |
$4$ |
$39$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$58.90795$ |
$\textsf{none}$ |
0 |
$\Z/13\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 13$ |
3B, 13B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$71447.18768$ |
0.641303 |
\( 7824861 a^{5} - 5363852 a^{4} - 38334375 a^{3} - 11300754 a^{2} + 16416844 a + 5946574 \) |
\( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 2\) , \( -3 a^{4} + 4 a^{3} + 12 a^{2} - 3 a - 4\) , \( 10 a^{5} - 28 a^{4} - 19 a^{3} + 67 a^{2} - 8 a - 15\bigr] \) |
${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-3\right){x}^{2}+\left(-3a^{4}+4a^{3}+12a^{2}-3a-4\right){x}+10a^{5}-28a^{4}-19a^{3}+67a^{2}-8a-15$ |
| 1.1-a4 |
1.1-a |
$4$ |
$39$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$58.90795$ |
$\textsf{none}$ |
0 |
$\Z/13\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 13$ |
3B, 13B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$71447.18768$ |
0.641303 |
\( -23419364 a^{5} + 64630767 a^{4} + 44556569 a^{3} - 150905488 a^{2} + 21033374 a + 30775655 \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 4 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( -3 a^{5} + 4 a^{4} + 15 a^{3} - 6 a^{2} - 17 a - 3\) , \( 3 a^{5} - 4 a^{4} - 15 a^{3} + 5 a^{2} + 16 a + 4\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+8a^{2}+4a-1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}-4\right){x}^{2}+\left(-3a^{5}+4a^{4}+15a^{3}-6a^{2}-17a-3\right){x}+3a^{5}-4a^{4}-15a^{3}+5a^{2}+16a+4$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$77.52722$ |
$(-2a^5+4a^4+7a^3-9a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$852.4945286$ |
1.29317 |
\( -\frac{3848949937}{27} a^{5} + 393492649 a^{4} + \frac{7318056002}{27} a^{3} - \frac{24808825474}{27} a^{2} + \frac{3466518662}{27} a + \frac{5062395074}{27} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2}\) , \( -a^{4} + a^{3} + 5 a^{2} - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( 8 a^{5} - 6 a^{4} - 38 a^{3} - 10 a^{2} + 16 a + 6\) , \( 69 a^{5} - 47 a^{4} - 338 a^{3} - 101 a^{2} + 144 a + 52\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3\right){x}^{2}+\left(8a^{5}-6a^{4}-38a^{3}-10a^{2}+16a+6\right){x}+69a^{5}-47a^{4}-338a^{3}-101a^{2}+144a+52$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$77.52722$ |
$(-2a^5+4a^4+7a^3-9a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$852.4945286$ |
1.29317 |
\( \frac{1055118509}{3} a^{5} - 244670120 a^{4} - \frac{5145769816}{3} a^{3} - \frac{1505650789}{3} a^{2} + \frac{2201965499}{3} a + \frac{796277816}{3} \) |
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 3\) , \( a^{5} - 4 a^{4} + 10 a^{2} - a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( -10 a^{5} + 13 a^{4} + 41 a^{3} - 9 a^{2} - 18 a + 1\) , \( -10 a^{5} + 10 a^{4} + 46 a^{3} - a^{2} - 20 a - 2\bigr] \) |
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-3\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+2a-2\right){y}={x}^{3}+\left(a^{5}-4a^{4}+10a^{2}-a-4\right){x}^{2}+\left(-10a^{5}+13a^{4}+41a^{3}-9a^{2}-18a+1\right){x}-10a^{5}+10a^{4}+46a^{3}-a^{2}-20a-2$ |
| 27.1-b1 |
27.1-b |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{15} \) |
$77.52722$ |
$(-2a^5+4a^4+7a^3-9a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$858.1016348$ |
1.30168 |
\( -\frac{11734585}{243} a^{5} + \frac{15715691}{243} a^{4} + \frac{57569735}{243} a^{3} - \frac{6959048}{81} a^{2} - \frac{20625952}{81} a - \frac{17771525}{243} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 12 a^{2} + a + 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 1\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 9 a^{2} - 5 a + 5\) , \( -18 a^{5} + 41 a^{4} + 60 a^{3} - 112 a^{2} - 32 a + 48\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+3a-1\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+5a^{3}-12a^{2}+a+4\right){x}^{2}+\left(-2a^{5}+4a^{4}+7a^{3}-9a^{2}-5a+5\right){x}-18a^{5}+41a^{4}+60a^{3}-112a^{2}-32a+48$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{9} \) |
$77.52722$ |
$(-2a^5+4a^4+7a^3-9a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$852.4945286$ |
1.29317 |
\( \frac{1286151805}{27} a^{5} - \frac{97850411}{3} a^{4} - \frac{6302966594}{27} a^{3} - \frac{1859319866}{27} a^{2} + \frac{2699241622}{27} a + \frac{977886878}{27} \) |
\( \bigl[a + 1\) , \( a^{5} - 4 a^{4} + 12 a^{2} - 3 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 6 a - 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 10 a^{2} - 3 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-1\right){y}={x}^{3}+\left(a^{5}-4a^{4}+12a^{2}-3a-4\right){x}^{2}+\left(-2a^{5}+3a^{4}+8a^{3}-6a-1\right){x}-3a^{5}+6a^{4}+10a^{3}-10a^{2}-3a$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{3} \) |
$77.52722$ |
$(-2a^5+4a^4+7a^3-9a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$852.4945286$ |
1.29317 |
\( -\frac{3164945057}{3} a^{5} + 2902622828 a^{4} + \frac{6076665952}{3} a^{3} - \frac{20306097035}{3} a^{2} + \frac{2731169941}{3} a + \frac{4107624116}{3} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 2\) , \( -a^{2} + a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -10 a^{5} + 23 a^{4} + 29 a^{3} - 48 a^{2} - 13 a + 2\) , \( -18 a^{5} + 38 a^{4} + 59 a^{3} - 78 a^{2} - 35 a\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+8a^{2}+5a-2\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a\right){x}^{2}+\left(-10a^{5}+23a^{4}+29a^{3}-48a^{2}-13a+2\right){x}-18a^{5}+38a^{4}+59a^{3}-78a^{2}-35a$ |
| 27.2-b1 |
27.2-b |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{15} \) |
$77.52722$ |
$(-2a^5+4a^4+7a^3-9a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$858.1016348$ |
1.30168 |
\( \frac{1612895}{243} a^{5} - \frac{688339}{27} a^{4} + \frac{4362505}{243} a^{3} + \frac{2436914}{243} a^{2} - \frac{72826}{27} a - \frac{317266}{81} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + 2 a + 1\) , \( -3 a^{5} + 8 a^{4} + 6 a^{3} - 18 a^{2} + a + 6\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( 11 a^{5} - 13 a^{4} - 58 a^{3} + 16 a^{2} + 61 a + 21\) , \( -560 a^{5} + 744 a^{4} + 2735 a^{3} - 952 a^{2} - 2871 a - 825\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+3a^{2}+2a+1\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){y}={x}^{3}+\left(-3a^{5}+8a^{4}+6a^{3}-18a^{2}+a+6\right){x}^{2}+\left(11a^{5}-13a^{4}-58a^{3}+16a^{2}+61a+21\right){x}-560a^{5}+744a^{4}+2735a^{3}-952a^{2}-2871a-825$ |
| 29.1-a1 |
29.1-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{5} \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$1.481331625$ |
1.40442 |
\( -\frac{114595298439097102868526844523731}{20511149} a^{5} + \frac{151675552625626526718826727580063}{20511149} a^{4} + \frac{560978222901143343582252842098390}{20511149} a^{3} - \frac{193517191812238007197441347247967}{20511149} a^{2} - \frac{589280924297514314247975153893832}{20511149} a - \frac{169413338416695988765174446920769}{20511149} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 4 a + 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -34 a^{5} + 81 a^{4} + 65 a^{3} - 117 a^{2} - 27 a + 6\) , \( -56 a^{5} + 163 a^{4} + 31 a^{3} - 264 a^{2} - 13 a + 30\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+4a+1\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-34a^{5}+81a^{4}+65a^{3}-117a^{2}-27a+6\right){x}-56a^{5}+163a^{4}+31a^{3}-264a^{2}-13a+30$ |
| 29.1-a2 |
29.1-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{15} \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$1.481331625$ |
1.40442 |
\( -\frac{1635650739851030120050444592454}{8629188747598184440949} a^{5} + \frac{143331287971873231350042950533}{8629188747598184440949} a^{4} + \frac{5370526781114582256956348957640}{8629188747598184440949} a^{3} + \frac{206666298492770208833511012406}{8629188747598184440949} a^{2} - \frac{4022326633841788552173132780163}{8629188747598184440949} a - \frac{1280775053522779070696447027161}{8629188747598184440949} \) |
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( -25 a^{5} + 65 a^{4} + 75 a^{3} - 170 a^{2} - 65 a + 5\) , \( -81 a^{5} + 262 a^{4} + 173 a^{3} - 737 a^{2} - 174 a + 41\bigr] \) |
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-1\right){x}^{2}+\left(-25a^{5}+65a^{4}+75a^{3}-170a^{2}-65a+5\right){x}-81a^{5}+262a^{4}+173a^{3}-737a^{2}-174a+41$ |
| 29.1-a3 |
29.1-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23145.80664$ |
1.40442 |
\( \frac{29493090}{29} a^{5} - \frac{103408610}{29} a^{4} + \frac{36642858}{29} a^{3} + \frac{97274296}{29} a^{2} - \frac{30413785}{29} a - \frac{21201649}{29} \) |
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - 2 a - 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -29 a^{5} + 67 a^{4} + 95 a^{3} - 175 a^{2} - 56 a + 79\) , \( -60 a^{5} + 141 a^{4} + 189 a^{3} - 364 a^{2} - 105 a + 158\bigr] \) |
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-2a-2\right){x}^{2}+\left(-29a^{5}+67a^{4}+95a^{3}-175a^{2}-56a+79\right){x}-60a^{5}+141a^{4}+189a^{3}-364a^{2}-105a+158$ |
| 29.1-a4 |
29.1-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{3} \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23145.80664$ |
1.40442 |
\( \frac{539594543}{24389} a^{5} - \frac{1283681989}{24389} a^{4} - \frac{1673905896}{24389} a^{3} + \frac{3331120832}{24389} a^{2} + \frac{906852221}{24389} a - \frac{1406061431}{24389} \) |
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-1\right){x}^{2}$ |
| 29.1-b1 |
29.1-b |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{7} \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$644.7601049$ |
0.978054 |
\( -\frac{489143918834519418}{17249876309} a^{5} + \frac{1350726974773319371}{17249876309} a^{4} + \frac{928906959941769094}{17249876309} a^{3} - \frac{3154651692992057986}{17249876309} a^{2} + \frac{442831889196161377}{17249876309} a + \frac{644411244050480300}{17249876309} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} + a - 3\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 10 a^{2} + 3 a + 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} + a - 3\) , \( 3 a^{5} - 9 a^{4} - 8 a^{3} + 29 a^{2} + 7 a - 15\) , \( -16 a^{5} + 35 a^{4} + 53 a^{3} - 84 a^{2} - 28 a + 32\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}+a-3\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}+a-3\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+4a^{3}-10a^{2}+3a+3\right){x}^{2}+\left(3a^{5}-9a^{4}-8a^{3}+29a^{2}+7a-15\right){x}-16a^{5}+35a^{4}+53a^{3}-84a^{2}-28a+32$ |
| 29.1-c1 |
29.1-c |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$790.5898677$ |
1.19927 |
\( \frac{109738396588016}{29} a^{5} - \frac{75141968632640}{29} a^{4} - \frac{537785028630652}{29} a^{3} - \frac{158636630089667}{29} a^{2} + \frac{230304788846590}{29} a + \frac{83434570141812}{29} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} + a - 3\) , \( 2 a^{5} - 6 a^{4} - 3 a^{3} + 15 a^{2} - 4 a - 6\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( 20 a^{5} - 49 a^{4} - 58 a^{3} + 125 a^{2} + 24 a - 46\) , \( 31 a^{5} - 75 a^{4} - 92 a^{3} + 193 a^{2} + 40 a - 78\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}+a-3\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-3a^{3}+15a^{2}-4a-6\right){x}^{2}+\left(20a^{5}-49a^{4}-58a^{3}+125a^{2}+24a-46\right){x}+31a^{5}-75a^{4}-92a^{3}+193a^{2}+40a-78$ |
| 29.1-d1 |
29.1-d |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.002329586$ |
$95834.38159$ |
2.03196 |
\( \frac{667554634}{29} a^{5} - \frac{1371543644}{29} a^{4} - \frac{2441773799}{29} a^{3} + \frac{3213179648}{29} a^{2} + \frac{1833046714}{29} a - \frac{936732887}{29} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + 3\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 1\) , \( -a^{5} + 2 a^{4} + 2 a^{3} - a^{2} + 2 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 2 a^{2} - 7 a + 1\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a\right){x}{y}+\left(2a^{5}-4a^{4}-7a^{3}+8a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+3\right){x}^{2}+\left(-a^{5}+2a^{4}+2a^{3}-a^{2}+2a-5\right){x}-a^{5}+a^{4}+6a^{3}-2a^{2}-7a+1$ |
| 29.1-d2 |
29.1-d |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{3} \) |
$77.99027$ |
$(a^4-a^3-4a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.000776528$ |
$95834.38159$ |
2.03196 |
\( \frac{500000491}{24389} a^{5} - \frac{1363317714}{24389} a^{4} - \frac{773050885}{24389} a^{3} + \frac{807170016}{24389} a^{2} + \frac{245432467}{24389} a - \frac{33725467}{24389} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - 5\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+3a-3\right){x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-3\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}-5\right){x}^{2}$ |
| 29.2-a1 |
29.2-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{5} \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$1.481331625$ |
1.40442 |
\( \frac{23990737415377332964630580910385}{20511149} a^{5} - \frac{83448470178538726713593050182342}{20511149} a^{4} + \frac{27404100394439215638449912012936}{20511149} a^{3} + \frac{79440505494694377085636578668150}{20511149} a^{2} - \frac{21478877574700214871390186433119}{20511149} a - \frac{16227917704608257854366710709033}{20511149} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( 105 a^{5} - 194 a^{4} - 403 a^{3} + 388 a^{2} + 317 a - 39\) , \( 274 a^{5} - 510 a^{4} - 1086 a^{3} + 1108 a^{2} + 922 a - 292\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+3a+1\right){x}^{2}+\left(105a^{5}-194a^{4}-403a^{3}+388a^{2}+317a-39\right){x}+274a^{5}-510a^{4}-1086a^{3}+1108a^{2}+922a-292$ |
| 29.2-a2 |
29.2-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{15} \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$1.481331625$ |
1.40442 |
\( \frac{49517926748131685406029400211528}{8629188747598184440949} a^{5} - \frac{118018847388936022519470695147732}{8629188747598184440949} a^{4} - \frac{152677702645431525968546689515834}{8629188747598184440949} a^{3} + \frac{305537605996119022369549489960117}{8629188747598184440949} a^{2} + \frac{81336262405475238261621776760232}{8629188747598184440949} a - \frac{129867942024508507713764721191699}{8629188747598184440949} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} - a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( 130 a^{5} - 309 a^{4} - 397 a^{3} + 796 a^{2} + 211 a - 347\) , \( 980 a^{5} - 2356 a^{4} - 3009 a^{3} + 6089 a^{2} + 1599 a - 2603\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}-a+3\right){x}^{2}+\left(130a^{5}-309a^{4}-397a^{3}+796a^{2}+211a-347\right){x}+980a^{5}-2356a^{4}-3009a^{3}+6089a^{2}+1599a-2603$ |
| 29.2-a3 |
29.2-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23145.80664$ |
1.40442 |
\( -\frac{144127121}{29} a^{5} + \frac{191914084}{29} a^{4} + \frac{703418442}{29} a^{3} - \frac{248156687}{29} a^{2} - \frac{735776072}{29} a - \frac{210483929}{29} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 3\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( -4 a^{5} + 8 a^{4} + 14 a^{3} - 15 a^{2} - 9 a - 1\) , \( 2 a^{5} - a^{4} - 13 a^{3} - 2 a^{2} + 15 a + 4\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+2a-3\right){x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+3a-3\right){x}^{2}+\left(-4a^{5}+8a^{4}+14a^{3}-15a^{2}-9a-1\right){x}+2a^{5}-a^{4}-13a^{3}-2a^{2}+15a+4$ |
| 29.2-a4 |
29.2-a |
$4$ |
$15$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{3} \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23145.80664$ |
1.40442 |
\( -\frac{5183334}{24389} a^{5} - \frac{23483887}{24389} a^{4} + \frac{12947976}{24389} a^{3} + \frac{55965587}{24389} a^{2} - \frac{18648968}{24389} a - \frac{11368635}{24389} \) |
\( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + 2 a - 4\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+2a-4\right){x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-1\right){x}^{2}$ |
| 29.2-b1 |
29.2-b |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{7} \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$644.7601049$ |
0.978054 |
\( \frac{163462751293821202}{17249876309} a^{5} - \frac{111681935365476176}{17249876309} a^{4} - \frac{801547698431869756}{17249876309} a^{3} - \frac{236802257690773383}{17249876309} a^{2} + \frac{343172721161084264}{17249876309} a + \frac{124367830204079372}{17249876309} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{3} - 2 a^{2} - a + 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\) , \( -a^{5} + 3 a^{4} + a^{3} - 6 a^{2} + a + 1\) , \( 2 a^{5} - 5 a^{4} - 4 a^{3} + 12 a^{2} - a - 4\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+4a-2\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+1\right){x}^{2}+\left(-a^{5}+3a^{4}+a^{3}-6a^{2}+a+1\right){x}+2a^{5}-5a^{4}-4a^{3}+12a^{2}-a-4$ |
| 29.2-c1 |
29.2-c |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$790.5898677$ |
1.19927 |
\( -\frac{328404104530776}{29} a^{5} + \frac{906495307821765}{29} a^{4} + \frac{624404013794482}{29} a^{3} - \frac{2116757679534948}{29} a^{2} + \frac{295763857235945}{29} a + \frac{431937635205700}{29} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a + 1\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 10 a^{2} + a + 1\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 2 a^{2} + 11 a + 4\) , \( 6 a^{5} - 8 a^{4} - 29 a^{3} + 11 a^{2} + 28 a + 6\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a+1\right){x}{y}+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+3a-3\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+4a^{3}-10a^{2}+a+1\right){x}^{2}+\left(2a^{5}-2a^{4}-11a^{3}+2a^{2}+11a+4\right){x}+6a^{5}-8a^{4}-29a^{3}+11a^{2}+28a+6$ |
| 29.2-d1 |
29.2-d |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{3} \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.000776528$ |
$95834.38159$ |
2.03196 |
\( \frac{2227643651}{24389} a^{5} - \frac{6600751439}{24389} a^{4} - \frac{5119963945}{24389} a^{3} + \frac{20357393301}{24389} a^{2} + \frac{411157352}{24389} a - \frac{13119189482}{24389} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 8 a^{2} - 5 a + 2\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{5} + 5 a^{3} + 6 a^{2} - 2 a - 3\) , \( -4 a^{5} + 4 a^{4} + 18 a^{3} + a^{2} - 8 a - 3\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+7a^{3}-8a^{2}-5a+2\right){x}^{2}+\left(-a^{5}+5a^{3}+6a^{2}-2a-3\right){x}-4a^{5}+4a^{4}+18a^{3}+a^{2}-8a-3$ |
| 29.2-d2 |
29.2-d |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$77.99027$ |
$(3a^5-7a^4-9a^3+17a^2+3a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.002329586$ |
$95834.38159$ |
2.03196 |
\( -\frac{48945886}{29} a^{5} + \frac{138712716}{29} a^{4} - \frac{41434329}{29} a^{3} - \frac{133295612}{29} a^{2} + \frac{35939234}{29} a + \frac{27409508}{29} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 5 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 3 a + 5\) , \( a^{5} - 8 a^{3} - a^{2} + 9 a + 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-4a^{2}-5a+2\right){x}^{2}+\left(a^{4}-3a^{3}-2a^{2}+3a+5\right){x}+a^{5}-8a^{3}-a^{2}+9a+5$ |
| 43.1-a1 |
43.1-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
43.1 |
\( 43 \) |
\( 43^{6} \) |
$80.59281$ |
$(-a^2-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$446.0334462$ |
1.35320 |
\( -\frac{123594015459941717}{6321363049} a^{5} + \frac{163867705234373064}{6321363049} a^{4} + \frac{604457441565415296}{6321363049} a^{3} - \frac{209658872549036511}{6321363049} a^{2} - \frac{634430342843747661}{6321363049} a - \frac{182189386830070682}{6321363049} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 2 a^{2} - 2 a + 2\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + 5 a^{3} - 12 a^{2} - 9 a + 6\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 15 a^{2} - 3 a + 5\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+3a-3\right){x}{y}+\left(2a^{5}-3a^{4}-8a^{3}+4a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-2a^{3}+2a^{2}-2a+2\right){x}^{2}+\left(-a^{5}+3a^{4}+5a^{3}-12a^{2}-9a+6\right){x}-2a^{5}+5a^{4}+5a^{3}-15a^{2}-3a+5$ |
| 43.1-a2 |
43.1-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
43.1 |
\( 43 \) |
\( 43^{2} \) |
$80.59281$ |
$(-a^2-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$446.0334462$ |
1.35320 |
\( -\frac{403066790528099641}{1849} a^{5} + \frac{1112587075378323065}{1849} a^{4} + \frac{766362210029610410}{1849} a^{3} - \frac{2598002611238589646}{1849} a^{2} + \frac{363005907177829822}{1849} a + \frac{530138604230001806}{1849} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 7 a^{5} - 17 a^{4} - 23 a^{3} + 48 a^{2} + 15 a - 22\) , \( 11 a^{5} - 24 a^{4} - 37 a^{3} + 66 a^{2} + 25 a - 32\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+8a^{2}+5a-1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+a-2\right){x}^{2}+\left(7a^{5}-17a^{4}-23a^{3}+48a^{2}+15a-22\right){x}+11a^{5}-24a^{4}-37a^{3}+66a^{2}+25a-32$ |
| 43.1-b1 |
43.1-b |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
43.1 |
\( 43 \) |
\( 43^{2} \) |
$80.59281$ |
$(-a^2-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.000860058$ |
$143341.2927$ |
2.24411 |
\( \frac{1173083203}{1849} a^{5} - \frac{2790286163}{1849} a^{4} - \frac{3629153135}{1849} a^{3} + \frac{7234904105}{1849} a^{2} + \frac{1921313797}{1849} a - \frac{3086043086}{1849} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 3\) , \( -2 a^{5} + 6 a^{4} + 3 a^{3} - 14 a^{2} + 3 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{5} - 3 a^{4} - a^{3} + 9 a^{2} - 4 a - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 6 a^{2} + 1\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+a-3\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+3a^{3}-14a^{2}+3a+5\right){x}^{2}+\left(a^{5}-3a^{4}-a^{3}+9a^{2}-4a-2\right){x}-a^{5}+3a^{4}+2a^{3}-6a^{2}+1$ |
| 43.2-a1 |
43.2-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
43.2 |
\( 43 \) |
\( 43^{6} \) |
$80.59281$ |
$(a^5-3a^4-a^3+7a^2-3a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$446.0334462$ |
1.35320 |
\( \frac{25867021722146251}{6321363049} a^{5} - \frac{89822684726406532}{6321363049} a^{4} + \frac{29268467321015368}{6321363049} a^{3} + \frac{85250804762932381}{6321363049} a^{2} - \frac{22977539272511937}{6321363049} a - \frac{17388365353799698}{6321363049} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 3 a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -3 a^{5} + 2 a^{4} + 16 a^{3} + 2 a^{2} - 9 a - 1\) , \( 9 a^{5} - 24 a^{4} - 27 a^{3} + 71 a^{2} + 19 a - 34\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-3\right){y}={x}^{3}+\left(a^{5}-4a^{4}+11a^{2}-3a-4\right){x}^{2}+\left(-3a^{5}+2a^{4}+16a^{3}+2a^{2}-9a-1\right){x}+9a^{5}-24a^{4}-27a^{3}+71a^{2}+19a-34$ |
| 43.2-a2 |
43.2-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
43.2 |
\( 43 \) |
\( 43^{2} \) |
$80.59281$ |
$(a^5-3a^4-a^3+7a^2-3a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$446.0334462$ |
1.35320 |
\( \frac{134687472447907851}{1849} a^{5} - \frac{92225553082493187}{1849} a^{4} - \frac{660050709979735846}{1849} a^{3} - \frac{194702637568708198}{1849} a^{2} + \frac{282664796987933702}{1849} a + \frac{102403485435484690}{1849} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a\) , \( 11 a^{5} - 13 a^{4} - 46 a^{3} + 7 a^{2} + 22 a + 6\) , \( 28 a^{5} - 24 a^{4} - 131 a^{3} - 19 a^{2} + 61 a + 20\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+3a^{2}+a\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(11a^{5}-13a^{4}-46a^{3}+7a^{2}+22a+6\right){x}+28a^{5}-24a^{4}-131a^{3}-19a^{2}+61a+20$ |
| 43.2-b1 |
43.2-b |
$1$ |
$1$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
43.2 |
\( 43 \) |
\( 43^{2} \) |
$80.59281$ |
$(a^5-3a^4-a^3+7a^2-3a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.000860058$ |
$143341.2927$ |
2.24411 |
\( -\frac{35119198}{1849} a^{5} + \frac{13127784}{1849} a^{4} + \frac{79757853}{1849} a^{3} - \frac{41392973}{1849} a^{2} - \frac{11112889}{1849} a + \frac{3697481}{1849} \) |
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} - 2 a^{4} + 13 a^{3} + 19 a^{2} - 4 a - 9\) , \( -13 a^{5} + 16 a^{4} + 56 a^{3} - 13 a^{2} - 25 a + 4\bigr] \) |
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-3\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+a-3\right){x}^{2}+\left(-2a^{5}-2a^{4}+13a^{3}+19a^{2}-4a-9\right){x}-13a^{5}+16a^{4}+56a^{3}-13a^{2}-25a+4$ |
| 49.1-a1 |
49.1-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$81.47485$ |
$(-a^5+4a^4-11a^2+3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.001804752$ |
$47699.10907$ |
2.35052 |
\( -988580 a^{5} + \frac{19264786}{7} a^{4} + \frac{12812783}{7} a^{3} - \frac{45131999}{7} a^{2} + \frac{6920425}{7} a + 1345334 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 2 a - 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 3\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 2 a^{2} - 5 a - 1\) , \( -3 a^{5} + 4 a^{4} + 12 a^{3} - a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-8a^{3}+4a^{2}+5a+1\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+a-3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-2a-2\right){x}^{2}+\left(-3a^{5}+4a^{4}+13a^{3}-2a^{2}-5a-1\right){x}-3a^{5}+4a^{4}+12a^{3}-a^{2}-4a-1$ |
| 49.1-a2 |
49.1-a |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$81.47485$ |
$(-a^5+4a^4-11a^2+3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.005414256$ |
$47699.10907$ |
2.35052 |
\( -\frac{33556156766}{7} a^{5} + 16674377390 a^{4} - \frac{38330968859}{7} a^{3} - \frac{111114623838}{7} a^{2} + \frac{30043261222}{7} a + \frac{22698372290}{7} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( -a^{5} + a^{4} + 4 a^{3} + a^{2} - 2 a - 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 4 a + 1\) , \( -5 a^{5} + 7 a^{4} + 20 a^{3} - 5 a^{2} - 13 a - 3\) , \( -a^{5} + a^{4} + 6 a^{3} + a^{2} - 8 a - 3\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+2a-2\right){x}{y}+\left(2a^{5}-3a^{4}-8a^{3}+4a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}+a^{2}-2a-1\right){x}^{2}+\left(-5a^{5}+7a^{4}+20a^{3}-5a^{2}-13a-3\right){x}-a^{5}+a^{4}+6a^{3}+a^{2}-8a-3$ |
| 49.1-b1 |
49.1-b |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$81.47485$ |
$(-a^5+4a^4-11a^2+3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.001804752$ |
$47699.10907$ |
2.35052 |
\( \frac{2333735}{7} a^{5} - \frac{1536755}{7} a^{4} - 1654035 a^{3} - \frac{3465769}{7} a^{2} + \frac{4986743}{7} a + \frac{1824569}{7} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a + 2\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a + 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a+2\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+a-3\right){x}^{2}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-11a+1\right){x}+2a^{5}-5a^{4}-5a^{3}+12a^{2}-4$ |
| 49.1-b2 |
49.1-b |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$81.47485$ |
$(-a^5+4a^4-11a^2+3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.005414256$ |
$47699.10907$ |
2.35052 |
\( \frac{160286323352}{7} a^{5} - 30307293282 a^{4} - \frac{784649541341}{7} a^{3} + \frac{270675690984}{7} a^{2} + \frac{824237004320}{7} a + \frac{236961171817}{7} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2}\) , \( 3 a^{5} - 8 a^{4} - 8 a^{3} + 21 a^{2} + 5 a - 7\) , \( -5 a^{5} + 13 a^{4} + 14 a^{3} - 36 a^{2} - 6 a + 15\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-8a^{3}+4a^{2}+5a-1\right){x}^{2}+\left(3a^{5}-8a^{4}-8a^{3}+21a^{2}+5a-7\right){x}-5a^{5}+13a^{4}+14a^{3}-36a^{2}-6a+15$ |
| 71.1-a1 |
71.1-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( -71 \) |
$84.03215$ |
$(2a^5-6a^4-4a^3+17a^2-a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$3633.522533$ |
1.37795 |
\( \frac{297477349}{71} a^{5} - \frac{837358584}{71} a^{4} - \frac{502474921}{71} a^{3} + \frac{1866551783}{71} a^{2} - \frac{278037049}{71} a - \frac{384949468}{71} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 2\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 2 a - 3\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 3 a^{5} - 10 a^{4} - 6 a^{3} + 31 a^{2} + 3 a - 14\) , \( 4 a^{5} - 9 a^{4} - 13 a^{3} + 22 a^{2} + 7 a - 10\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+a-2\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a-1\right){y}={x}^{3}+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+2a-3\right){x}^{2}+\left(3a^{5}-10a^{4}-6a^{3}+31a^{2}+3a-14\right){x}+4a^{5}-9a^{4}-13a^{3}+22a^{2}+7a-10$ |
| 71.1-a2 |
71.1-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{3} \) |
$84.03215$ |
$(2a^5-6a^4-4a^3+17a^2-a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$3633.522533$ |
1.37795 |
\( -\frac{191935393}{357911} a^{5} - \frac{580390420}{357911} a^{4} + \frac{436997224}{357911} a^{3} + \frac{785354329}{357911} a^{2} - \frac{527031693}{357911} a + \frac{334971338}{357911} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( -a^{5} + 6 a^{3} + 4 a^{2} - 3 a - 2\) , \( 0\) , \( -4 a^{5} + 3 a^{4} + 19 a^{3} + 5 a^{2} - 7 a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-1\right){x}{y}={x}^{3}+\left(-a^{5}+6a^{3}+4a^{2}-3a-2\right){x}^{2}+\left(-4a^{5}+3a^{4}+19a^{3}+5a^{2}-7a-2\right){x}$ |
| 71.1-a3 |
71.1-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{6} \) |
$84.03215$ |
$(2a^5-6a^4-4a^3+17a^2-a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$1816.761266$ |
1.37795 |
\( \frac{14623190787592690023}{128100283921} a^{5} + \frac{9262831648934631201}{128100283921} a^{4} - \frac{34215233218956422760}{128100283921} a^{3} - \frac{17202576339060202666}{128100283921} a^{2} + \frac{13171892585884276804}{128100283921} a + \frac{5541195868726527748}{128100283921} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 6 a^{2} - 3 a - 2\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 10 a^{5} - 30 a^{4} - 10 a^{3} + 51 a^{2} - a - 14\) , \( -15 a^{5} + 55 a^{4} - 31 a^{3} - 39 a^{2} + 17 a + 6\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+3a-2\right){x}{y}+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-a^{3}+6a^{2}-3a-2\right){x}^{2}+\left(10a^{5}-30a^{4}-10a^{3}+51a^{2}-a-14\right){x}-15a^{5}+55a^{4}-31a^{3}-39a^{2}+17a+6$ |
| 71.1-a4 |
71.1-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{2} \) |
$84.03215$ |
$(2a^5-6a^4-4a^3+17a^2-a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$1816.761266$ |
1.37795 |
\( -\frac{7067022792014335}{5041} a^{5} + \frac{24612619416466217}{5041} a^{4} - \frac{8158647124759995}{5041} a^{3} - \frac{23426232526371070}{5041} a^{2} + \frac{6414105640727850}{5041} a + \frac{4812827440073893}{5041} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a + 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 11 a^{2} - a + 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a\) , \( -97 a^{5} + 157 a^{4} + 417 a^{3} - 259 a^{2} - 387 a - 94\) , \( -599 a^{5} + 877 a^{4} + 2755 a^{3} - 1288 a^{2} - 2719 a - 723\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+3a^{2}+a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+3a^{2}+a\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+5a^{3}-11a^{2}-a+2\right){x}^{2}+\left(-97a^{5}+157a^{4}+417a^{3}-259a^{2}-387a-94\right){x}-599a^{5}+877a^{4}+2755a^{3}-1288a^{2}-2719a-723$ |
| 71.1-b1 |
71.1-b |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71^{3} \) |
$84.03215$ |
$(2a^5-6a^4-4a^3+17a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$9.122861674$ |
1.12094 |
\( -\frac{25415776248234932727}{357911} a^{5} + \frac{33644549177505288315}{357911} a^{4} + \frac{124407707776619205840}{357911} a^{3} - \frac{42935695592915487066}{357911} a^{2} - \frac{130674592083511357736}{357911} a - \frac{37564287471550457576}{357911} \) |
\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( -a^{5} + 6 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -297 a^{5} + 798 a^{4} + 604 a^{3} - 1840 a^{2} + 208 a + 366\) , \( -3433 a^{5} + 9442 a^{4} + 6587 a^{3} - 22010 a^{2} + 3003 a + 4476\bigr] \) |
${y}^2+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+4a-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(-297a^{5}+798a^{4}+604a^{3}-1840a^{2}+208a+366\right){x}-3433a^{5}+9442a^{4}+6587a^{3}-22010a^{2}+3003a+4476$ |
| 71.1-b2 |
71.1-b |
$2$ |
$3$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$84.03215$ |
$(2a^5-6a^4-4a^3+17a^2-a-6)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6650.566160$ |
1.12094 |
\( \frac{5253651}{71} a^{5} - \frac{13681584}{71} a^{4} - \frac{14298038}{71} a^{3} + \frac{37562313}{71} a^{2} + \frac{4849167}{71} a - \frac{18566036}{71} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 4 a - 1\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 3 a - 4\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 3\) , \( -3 a^{5} + 6 a^{4} + 9 a^{3} - 9 a^{2} - 3 a\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} + a - 1\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+8a^{2}+4a-1\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+7a^{2}-3a-4\right){x}^{2}+\left(-3a^{5}+6a^{4}+9a^{3}-9a^{2}-3a\right){x}-a^{5}+2a^{4}+3a^{3}-4a^{2}+a-1$ |
| 71.2-a1 |
71.2-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( -71 \) |
$84.03215$ |
$(a^3-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$3952.270184$ |
1.49883 |
\( -\frac{771436057367340}{71} a^{5} + \frac{1021204229550191}{71} a^{4} + \frac{3776605848171226}{71} a^{3} - \frac{1302945474751863}{71} a^{2} - \frac{3967265080250394}{71} a - \frac{1140546291203617}{71} \) |
\( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( -5 a^{5} + 14 a^{4} + 8 a^{3} - 25 a^{2} + 6\) , \( a^{5} + a^{4} - 11 a^{3} - a^{2} + 18 a - 8\bigr] \) |
${y}^2+a{x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-4a^{2}-4a+2\right){x}^{2}+\left(-5a^{5}+14a^{4}+8a^{3}-25a^{2}+6\right){x}+a^{5}+a^{4}-11a^{3}-a^{2}+18a-8$ |
| 71.2-a2 |
71.2-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{3} \) |
$84.03215$ |
$(a^3-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$3952.270184$ |
1.49883 |
\( \frac{1334490057051325}{357911} a^{5} - \frac{3683030066630924}{357911} a^{4} - \frac{2539374775289438}{357911} a^{3} + \frac{8601694812985271}{357911} a^{2} - \frac{1197153818502630}{357911} a - \frac{1757930401343265}{357911} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 4\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 3\) , \( 11 a^{5} - 15 a^{4} - 45 a^{3} + 17 a^{2} + 18 a - 6\) , \( -14 a^{5} + 9 a^{4} + 66 a^{3} + 31 a^{2} - 27 a - 17\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-2\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-3\right){y}={x}^{3}+\left(a^{5}-4a^{4}+10a^{2}-2a-4\right){x}^{2}+\left(11a^{5}-15a^{4}-45a^{3}+17a^{2}+18a-6\right){x}-14a^{5}+9a^{4}+66a^{3}+31a^{2}-27a-17$ |
| 71.2-a3 |
71.2-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{6} \) |
$84.03215$ |
$(a^3-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$1976.135092$ |
1.49883 |
\( -\frac{8500387879565336175035396}{128100283921} a^{5} + \frac{20235904530522024705399019}{128100283921} a^{4} + \frac{26300093073516992002530478}{128100283921} a^{3} - \frac{52511461694779628562689886}{128100283921} a^{2} - \frac{14016610250085351570415344}{128100283921} a + \frac{22335446708020793502460695}{128100283921} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 4\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 3\) , \( 46 a^{5} - 110 a^{4} - 120 a^{3} + 232 a^{2} + 53 a - 96\) , \( 44 a^{5} - 93 a^{4} - 283 a^{3} + 570 a^{2} + 181 a - 275\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-2\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-3\right){y}={x}^{3}+\left(a^{5}-4a^{4}+10a^{2}-2a-4\right){x}^{2}+\left(46a^{5}-110a^{4}-120a^{3}+232a^{2}+53a-96\right){x}+44a^{5}-93a^{4}-283a^{3}+570a^{2}+181a-275$ |
| 71.2-a4 |
71.2-a |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{2} \) |
$84.03215$ |
$(a^3-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$1976.135092$ |
1.49883 |
\( \frac{2427847058697256047703464284364}{5041} a^{5} - \frac{3213439376084993538620895804626}{5041} a^{4} - \frac{11885036707571320938161451911154}{5041} a^{3} + \frac{4099907686861892112740975364149}{5041} a^{2} + \frac{12484665412014987227895045256073}{5041} a + \frac{3589236914441632306388327741777}{5041} \) |
\( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( 20 a^{5} - 51 a^{4} - 52 a^{3} + 120 a^{2} + 55 a - 84\) , \( 251 a^{5} - 630 a^{4} - 644 a^{3} + 1463 a^{2} + 269 a - 526\bigr] \) |
${y}^2+a{x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-4a^{2}-4a+2\right){x}^{2}+\left(20a^{5}-51a^{4}-52a^{3}+120a^{2}+55a-84\right){x}+251a^{5}-630a^{4}-644a^{3}+1463a^{2}+269a-526$ |
| 71.2-b1 |
71.2-b |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{2} \) |
$84.03215$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.097983788$ |
$5981.573738$ |
2.66720 |
\( -\frac{58168686536343316256911}{5041} a^{5} + \frac{39830276056343603859101}{5041} a^{4} + \frac{285062017990100061908014}{5041} a^{3} + \frac{84087973968099499538051}{5041} a^{2} - \frac{122076980141719179710154}{5041} a - \frac{44225911390155224771855}{5041} \) |
\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( 10 a^{5} - 30 a^{4} - 16 a^{3} + 72 a^{2} - 2 a - 32\) , \( a^{5} + 3 a^{4} - 24 a^{3} + 25 a^{2} + 18 a - 26\bigr] \) |
${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+3a-3\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-1\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}-4\right){x}^{2}+\left(10a^{5}-30a^{4}-16a^{3}+72a^{2}-2a-32\right){x}+a^{5}+3a^{4}-24a^{3}+25a^{2}+18a-26$ |
| 71.2-b2 |
71.2-b |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( -71 \) |
$84.03215$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.048991894$ |
$23926.29495$ |
2.66720 |
\( -\frac{84000971603}{71} a^{5} + \frac{57517542611}{71} a^{4} + \frac{411657827582}{71} a^{3} + \frac{121435286319}{71} a^{2} - \frac{176292213523}{71} a - \frac{63867521529}{71} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 8 a^{2} - 5 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a - 1\) , \( 3 a^{5} - 5 a^{4} - 12 a^{3} + 9 a^{2} + 7 a - 2\) , \( 6 a^{5} - 16 a^{4} - 17 a^{3} + 45 a^{2} + 9 a - 20\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a-1\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+7a^{3}-8a^{2}-5a+1\right){x}^{2}+\left(3a^{5}-5a^{4}-12a^{3}+9a^{2}+7a-2\right){x}+6a^{5}-16a^{4}-17a^{3}+45a^{2}+9a-20$ |
| 71.2-b3 |
71.2-b |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{3} \) |
$84.03215$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.016330631$ |
$23926.29495$ |
2.66720 |
\( \frac{19503808031}{357911} a^{5} - \frac{53829939140}{357911} a^{4} - \frac{36653092470}{357911} a^{3} + \frac{126101211770}{357911} a^{2} - \frac{17962351604}{357911} a - \frac{25733383533}{357911} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 12 a^{2} - 5 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 4 a^{2} - 5 a + 2\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} + 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(-3a^{5}+6a^{4}+10a^{3}-12a^{2}-5a+3\right){x}^{2}+\left(-2a^{5}+3a^{4}+8a^{3}-4a^{2}-5a+2\right){x}-a^{5}+2a^{4}+3a^{3}-4a^{2}+2$ |
| 71.2-b4 |
71.2-b |
$4$ |
$6$ |
6.6.434581.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{6} \) |
$84.03215$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.032661262$ |
$5981.573738$ |
2.66720 |
\( \frac{761638833101910810}{128100283921} a^{5} + \frac{556381569549059781}{128100283921} a^{4} - \frac{1637664927517631470}{128100283921} a^{3} - \frac{856118405892448540}{128100283921} a^{2} + \frac{648706548947243049}{128100283921} a + \frac{275925918956956389}{128100283921} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 12 a^{2} - 5 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} + 3 a^{4} + 13 a^{3} - 9 a^{2} - 25 a - 8\) , \( 11 a^{5} - 17 a^{4} - 50 a^{3} + 24 a^{2} + 58 a + 16\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(-3a^{5}+6a^{4}+10a^{3}-12a^{2}-5a+3\right){x}^{2}+\left(-2a^{5}+3a^{4}+13a^{3}-9a^{2}-25a-8\right){x}+11a^{5}-17a^{4}-50a^{3}+24a^{2}+58a+16$ |
*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.
