| 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 |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$122.00479$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1396.772303$ |
1.22859 |
\( -\frac{182007487}{9} a^{5} + \frac{291777437}{27} a^{4} + \frac{364014974}{3} a^{3} - \frac{912864724}{27} a^{2} - \frac{3021889742}{27} a + \frac{1318762211}{27} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 1\) , \( a^{4} - 5 a^{2} + 2\) , \( 13 a^{5} - 17 a^{4} - 73 a^{3} + 82 a^{2} + 71 a - 65\) , \( 50 a^{5} - 54 a^{4} - 290 a^{3} + 259 a^{2} + 300 a - 253\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+2\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+1\right){x}^{2}+\left(13a^{5}-17a^{4}-73a^{3}+82a^{2}+71a-65\right){x}+50a^{5}-54a^{4}-290a^{3}+259a^{2}+300a-253$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( 17^{5} \) |
$128.64535$ |
$(-a^5-a^4+6a^3+6a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9216.864509$ |
2.02678 |
\( \frac{705100322749268}{1419857} a^{5} - \frac{765197685904218}{1419857} a^{4} - \frac{3352470798318183}{1419857} a^{3} + \frac{2855999422859987}{1419857} a^{2} + \frac{945576635464231}{1419857} a - \frac{734499198788826}{1419857} \) |
\( \bigl[a^{4} - 4 a^{2} - 2 a\) , \( -2 a^{5} - a^{4} + 11 a^{3} + 7 a^{2} - 4 a - 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 2 a + 1\) , \( -11 a^{5} - 9 a^{4} + 59 a^{3} + 55 a^{2} - 29 a - 22\) , \( -11 a^{5} - 6 a^{4} + 56 a^{3} + 30 a^{2} - 40 a - 14\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-2a\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+11a^{3}+7a^{2}-4a-3\right){x}^{2}+\left(-11a^{5}-9a^{4}+59a^{3}+55a^{2}-29a-22\right){x}-11a^{5}-6a^{4}+56a^{3}+30a^{2}-40a-14$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{10} \) |
$128.64535$ |
$(-a^5-a^4+6a^3+6a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1152.108063$ |
2.02678 |
\( -\frac{36117770875069273804931183957}{2015993900449} a^{5} + \frac{15622378720003666909827063050}{2015993900449} a^{4} + \frac{209949322376907640467936226575}{2015993900449} a^{3} - \frac{54693698011582630769717422098}{2015993900449} a^{2} - \frac{193049415979369023798685327771}{2015993900449} a + \frac{83501584259328827224915265639}{2015993900449} \) |
\( \bigl[a^{4} - 4 a^{2} - 2 a\) , \( -2 a^{5} - a^{4} + 11 a^{3} + 7 a^{2} - 4 a - 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 2 a + 1\) , \( 34 a^{5} + 6 a^{4} - 191 a^{3} - 70 a^{2} + 111 a - 22\) , \( 71 a^{5} + 146 a^{4} - 333 a^{3} - 850 a^{2} - 200 a + 277\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-2a\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+11a^{3}+7a^{2}-4a-3\right){x}^{2}+\left(34a^{5}+6a^{4}-191a^{3}-70a^{2}+111a-22\right){x}+71a^{5}+146a^{4}-333a^{3}-850a^{2}-200a+277$ |
| 17.2-a1 |
17.2-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$128.64535$ |
$(a^5-5a^3-2a^2+a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7909.055147$ |
1.73919 |
\( \frac{325456382}{17} a^{5} + \frac{255271243}{17} a^{4} - \frac{1866971681}{17} a^{3} - \frac{1798723008}{17} a^{2} + \frac{1207589207}{17} a + \frac{1103908428}{17} \) |
\( \bigl[a^{5} - 5 a^{3} - a^{2} + a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 1\) , \( a + 1\) , \( -a^{5} - 2 a^{4} + 7 a^{3} + 9 a^{2} - 2 a - 1\) , \( 2 a^{5} - 8 a^{3} - 6 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-a^{2}+a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-6a+1\right){x}^{2}+\left(-a^{5}-2a^{4}+7a^{3}+9a^{2}-2a-1\right){x}+2a^{5}-8a^{3}-6a^{2}+a+1$ |
| 17.2-a2 |
17.2-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{2} \) |
$128.64535$ |
$(a^5-5a^3-2a^2+a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3954.527573$ |
1.73919 |
\( -\frac{41049612397447503}{289} a^{5} + \frac{17757624077129184}{289} a^{4} + \frac{238612684602265397}{289} a^{3} - \frac{62163742825720689}{289} a^{2} - \frac{219403616703462308}{289} a + \frac{94901321640176039}{289} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 5 a + 2\) , \( -406 a^{5} + 486 a^{4} + 1865 a^{3} - 1826 a^{2} - 305 a + 344\) , \( 9329 a^{5} - 11072 a^{4} - 42798 a^{3} + 41456 a^{2} + 6600 a - 7839\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+5a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-406a^{5}+486a^{4}+1865a^{3}-1826a^{2}-305a+344\right){x}+9329a^{5}-11072a^{4}-42798a^{3}+41456a^{2}+6600a-7839$ |
| 17.3-a1 |
17.3-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.3 |
\( 17 \) |
\( 17^{5} \) |
$128.64535$ |
$(a^4-5a^2-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9216.864509$ |
2.02678 |
\( -\frac{1218563842128955}{1419857} a^{5} - \frac{1030086369816053}{1419857} a^{4} + \frac{6433251914596305}{1419857} a^{3} + \frac{6633884375121055}{1419857} a^{2} - \frac{1717610176642395}{1419857} a - \frac{1445700164082411}{1419857} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a\) , \( a^{5} - 6 a^{3} + 4 a - 2\) , \( 7 a^{5} - 7 a^{4} - 20 a^{3} - 3 a^{2} + 3 a + 2\) , \( 12 a^{5} - 49 a^{4} + 37 a^{3} + 33 a^{2} - 7 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-6a^{3}+4a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a\right){x}^{2}+\left(7a^{5}-7a^{4}-20a^{3}-3a^{2}+3a+2\right){x}+12a^{5}-49a^{4}+37a^{3}+33a^{2}-7a-7$ |
| 17.3-a2 |
17.3-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{10} \) |
$128.64535$ |
$(a^4-5a^2-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1152.108063$ |
2.02678 |
\( \frac{1264229249997728229176423981}{2015993900449} a^{5} + \frac{2922803433370096884313772245}{2015993900449} a^{4} - \frac{828072626478367013407666719}{2015993900449} a^{3} - \frac{3178671130214642625231994401}{2015993900449} a^{2} + \frac{236525700637532125770692596}{2015993900449} a + \frac{546829666019404710184643642}{2015993900449} \) |
\( \bigl[a^{5} - 6 a^{3} + 4 a - 2\) , \( -a^{5} - a^{4} + 6 a^{3} + 7 a^{2} - 5 a - 4\) , \( a^{5} - 5 a^{3} - a^{2} + 2 a\) , \( 9 a^{5} + 8 a^{4} - 73 a^{3} - 38 a^{2} + 107 a - 31\) , \( -64 a^{5} + 73 a^{4} + 314 a^{3} - 266 a^{2} - 89 a + 67\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+4a-2\right){x}{y}+\left(a^{5}-5a^{3}-a^{2}+2a\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+7a^{2}-5a-4\right){x}^{2}+\left(9a^{5}+8a^{4}-73a^{3}-38a^{2}+107a-31\right){x}-64a^{5}+73a^{4}+314a^{3}-266a^{2}-89a+67$ |
| 17.4-a1 |
17.4-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.4 |
\( 17 \) |
\( 17 \) |
$128.64535$ |
$(a^5+a^4-5a^3-7a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7909.055147$ |
1.73919 |
\( -\frac{24721824}{17} a^{5} + \frac{58360832}{17} a^{4} + \frac{62564333}{17} a^{3} - \frac{70171925}{17} a^{2} - \frac{17548492}{17} a + \frac{8212573}{17} \) |
\( \bigl[a^{5} - 5 a^{3} - a^{2} + a\) , \( -2 a^{5} + a^{4} + 11 a^{3} - 3 a^{2} - 7 a + 2\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( -10 a^{5} - 4 a^{4} + 58 a^{3} + 32 a^{2} - 44 a - 11\) , \( -14 a^{5} - 4 a^{4} + 80 a^{3} + 38 a^{2} - 58 a - 19\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-a^{2}+a\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+6a+1\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+11a^{3}-3a^{2}-7a+2\right){x}^{2}+\left(-10a^{5}-4a^{4}+58a^{3}+32a^{2}-44a-11\right){x}-14a^{5}-4a^{4}+80a^{3}+38a^{2}-58a-19$ |
| 17.4-a2 |
17.4-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
17.4 |
\( 17 \) |
\( - 17^{2} \) |
$128.64535$ |
$(a^5+a^4-5a^3-7a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3954.527573$ |
1.73919 |
\( \frac{1458256936165832}{289} a^{5} + \frac{3332389239606912}{289} a^{4} - \frac{1064551834575371}{289} a^{3} - \frac{3694968296678120}{289} a^{2} + \frac{356826080317857}{289} a + \frac{664922832622786}{289} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 4 a + 1\) , \( a^{4} - 6 a^{2} + 4\) , \( a^{5} - 5 a^{3} - a^{2} + a + 1\) , \( 24 a^{5} - 128 a^{3} - 29 a^{2} + 76 a - 23\) , \( -9 a^{5} - 43 a^{4} + 54 a^{3} + 215 a^{2} + 46 a - 99\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+4a+1\right){x}{y}+\left(a^{5}-5a^{3}-a^{2}+a+1\right){y}={x}^{3}+\left(a^{4}-6a^{2}+4\right){x}^{2}+\left(24a^{5}-128a^{3}-29a^{2}+76a-23\right){x}-9a^{5}-43a^{4}+54a^{3}+215a^{2}+46a-99$ |
| 37.1-a1 |
37.1-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{5} \) |
$137.25879$ |
$(-a^5-a^4+5a^3+6a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.013758992$ |
$9354.332616$ |
3.39627 |
\( \frac{1265612746744701}{69343957} a^{5} - \frac{2563954674742030}{69343957} a^{4} - \frac{2399817288427565}{69343957} a^{3} + \frac{3596662443771014}{69343957} a^{2} + \frac{308383628511699}{69343957} a - \frac{624766696006965}{69343957} \) |
\( \bigl[-a^{5} + 5 a^{3} + 2 a^{2} - 2 a - 2\) , \( 3 a^{5} - a^{4} - 16 a^{3} + a^{2} + 8 a - 1\) , \( a^{5} - 6 a^{3} + 4 a - 2\) , \( -5 a^{5} + 7 a^{4} + 23 a^{3} - 28 a^{2} - 2 a + 8\) , \( -73 a^{5} + 90 a^{4} + 332 a^{3} - 341 a^{2} - 41 a + 63\bigr] \) |
${y}^2+\left(-a^{5}+5a^{3}+2a^{2}-2a-2\right){x}{y}+\left(a^{5}-6a^{3}+4a-2\right){y}={x}^{3}+\left(3a^{5}-a^{4}-16a^{3}+a^{2}+8a-1\right){x}^{2}+\left(-5a^{5}+7a^{4}+23a^{3}-28a^{2}-2a+8\right){x}-73a^{5}+90a^{4}+332a^{3}-341a^{2}-41a+63$ |
| 37.2-a1 |
37.2-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
37.2 |
\( 37 \) |
\( 37^{5} \) |
$137.25879$ |
$(2a^5-11a^3-2a^2+6a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.013758992$ |
$9354.332616$ |
3.39627 |
\( -\frac{21313907625545309}{69343957} a^{5} - \frac{10521452857936465}{69343957} a^{4} + \frac{122689586561231213}{69343957} a^{3} + \frac{81878670098422069}{69343957} a^{2} - \frac{87464450489836244}{69343957} a - \frac{43175896603132934}{69343957} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{4} - 5 a^{2} - a + 2\) , \( 4 a^{5} - 24 a^{3} + 2 a^{2} + 21 a - 8\) , \( -13 a^{5} + 6 a^{4} + 70 a^{3} - 21 a^{2} - 65 a + 29\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(4a^{5}-24a^{3}+2a^{2}+21a-8\right){x}-13a^{5}+6a^{4}+70a^{3}-21a^{2}-65a+29$ |
| 53.1-a1 |
53.1-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.1 |
\( 53 \) |
\( 53 \) |
$141.43156$ |
$(-a^5-a^4+5a^3+7a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.279149990$ |
$3066.445409$ |
4.51758 |
\( \frac{1307956473}{53} a^{5} + \frac{1099954728}{53} a^{4} - \frac{6921782660}{53} a^{3} - \frac{7129279147}{53} a^{2} + \frac{1847696646}{53} a + \frac{1554186281}{53} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a\) , \( -a^{4} + 5 a^{2} + 2 a - 2\) , \( 1\) , \( 2 a^{5} - 4 a^{4} - 9 a^{3} + 18 a^{2} - a - 3\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 14 a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-2\right){x}^{2}+\left(2a^{5}-4a^{4}-9a^{3}+18a^{2}-a-3\right){x}+3a^{5}-4a^{4}-13a^{3}+14a^{2}+2a-3$ |
| 53.1-b1 |
53.1-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.1 |
\( 53 \) |
\( - 53^{3} \) |
$141.43156$ |
$(-a^5-a^4+5a^3+7a^2-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$18.62592350$ |
1.32704 |
\( \frac{1752169386252287065578330059913}{148877} a^{5} - \frac{757883254401290341901951018769}{148877} a^{4} - \frac{10185201534417639040973067255516}{148877} a^{3} + \frac{2653337151074009971312006273343}{148877} a^{2} + \frac{9365342005396574456870230220132}{148877} a - \frac{4050884539657786791047363220265}{148877} \) |
\( \bigl[-a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 3 a - 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 2 a\) , \( 9 a^{5} - 9 a^{4} - 41 a^{3} + 24 a^{2} + 32 a - 18\) , \( 22 a^{5} - 29 a^{4} - 69 a^{3} + 35 a^{2} + 61 a - 30\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-3a+1\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-2a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-3a-1\right){x}^{2}+\left(9a^{5}-9a^{4}-41a^{3}+24a^{2}+32a-18\right){x}+22a^{5}-29a^{4}-69a^{3}+35a^{2}+61a-30$ |
| 53.1-b2 |
53.1-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.1 |
\( 53 \) |
\( -53 \) |
$141.43156$ |
$(-a^5-a^4+5a^3+7a^2-a-4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$13578.29823$ |
1.32704 |
\( \frac{4864904250}{53} a^{5} - \frac{2104350663}{53} a^{4} - \frac{28281492602}{53} a^{3} + \frac{7367296554}{53} a^{2} + \frac{26005509969}{53} a - \frac{11248291631}{53} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + a + 3\) , \( -a^{4} - a^{3} + 6 a^{2} + 4 a - 5\) , \( a^{5} - 6 a^{3} + 4 a - 1\) , \( a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 6 a + 4\) , \( -a^{4} + a^{3} + 4 a^{2} - 2\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+a+3\right){x}{y}+\left(a^{5}-6a^{3}+4a-1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+4a-5\right){x}^{2}+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+6a+4\right){x}-a^{4}+a^{3}+4a^{2}-2$ |
| 53.1-c1 |
53.1-c |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.1 |
\( 53 \) |
\( 53 \) |
$141.43156$ |
$(-2a^5+11a^3+2a^2-6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$748.6889173$ |
0.658542 |
\( \frac{3158288480}{53} a^{5} + \frac{2397823537}{53} a^{4} - \frac{7575922920}{53} a^{3} + \frac{1820938547}{53} a^{2} + \frac{1318707641}{53} a - \frac{419423593}{53} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 2 a^{2} + 7 a + 1\) , \( a^{5} - 4 a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{5} - 6 a^{3} + 4 a - 1\) , \( -2 a^{5} - 8 a^{4} + 16 a^{3} + 40 a^{2} - 19 a - 11\) , \( -a^{5} - 8 a^{4} + 12 a^{3} + 38 a^{2} - 23 a - 15\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-2a^{2}+7a+1\right){x}{y}+\left(a^{5}-6a^{3}+4a-1\right){y}={x}^3+\left(a^{5}-4a^{3}-2a^{2}-3a+2\right){x}^2+\left(-2a^{5}-8a^{4}+16a^{3}+40a^{2}-19a-11\right){x}-a^{5}-8a^{4}+12a^{3}+38a^{2}-23a-15$ |
| 53.2-a1 |
53.2-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.2 |
\( 53 \) |
\( 53 \) |
$141.43156$ |
$(-2a^5+11a^3+3a^2-7a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.279149990$ |
$3066.445409$ |
4.51758 |
\( -\frac{655649604}{53} a^{5} + \frac{778405694}{53} a^{4} + \frac{3007941446}{53} a^{3} - \frac{2914829832}{53} a^{2} - \frac{464522723}{53} a + \frac{550848255}{53} \) |
\( \bigl[-a^{3} + a^{2} + 4 a - 1\) , \( -2 a^{5} + a^{4} + 11 a^{3} - 3 a^{2} - 7 a + 3\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a\) , \( 3 a^{5} + 3 a^{4} - 17 a^{3} - 20 a^{2} + 10 a + 14\) , \( -4 a^{5} - a^{4} + 23 a^{3} + 10 a^{2} - 17 a - 4\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a-1\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+6a\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+11a^{3}-3a^{2}-7a+3\right){x}^{2}+\left(3a^{5}+3a^{4}-17a^{3}-20a^{2}+10a+14\right){x}-4a^{5}-a^{4}+23a^{3}+10a^{2}-17a-4$ |
| 53.2-b1 |
53.2-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.2 |
\( 53 \) |
\( - 53^{3} \) |
$141.43156$ |
$(-2a^5+11a^3+3a^2-7a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$18.62592350$ |
1.32704 |
\( -\frac{61331132058061836479777465657}{148877} a^{5} - \frac{141792989081445014521369779358}{148877} a^{4} + \frac{40172009252287666381751689980}{148877} a^{3} + \frac{154205812145441581706045123036}{148877} a^{2} - \frac{11474490942712954954146450725}{148877} a - \frac{26528164642631474266962679837}{148877} \) |
\( \bigl[-a^{3} + a^{2} + 3 a - 2\) , \( -3 a^{5} - a^{4} + 16 a^{3} + 9 a^{2} - 6 a - 3\) , \( a^{5} - 6 a^{3} - a^{2} + 5 a + 1\) , \( -57 a^{5} - 28 a^{4} + 325 a^{3} + 211 a^{2} - 221 a - 90\) , \( -173 a^{5} - 70 a^{4} + 992 a^{3} + 565 a^{2} - 720 a - 260\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+3a-2\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+5a+1\right){y}={x}^{3}+\left(-3a^{5}-a^{4}+16a^{3}+9a^{2}-6a-3\right){x}^{2}+\left(-57a^{5}-28a^{4}+325a^{3}+211a^{2}-221a-90\right){x}-173a^{5}-70a^{4}+992a^{3}+565a^{2}-720a-260$ |
| 53.2-b2 |
53.2-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.2 |
\( 53 \) |
\( -53 \) |
$141.43156$ |
$(-2a^5+11a^3+3a^2-7a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$13578.29823$ |
1.32704 |
\( -\frac{159331194}{53} a^{5} - \frac{393903174}{53} a^{4} + \frac{48054266}{53} a^{3} + \frac{418399575}{53} a^{2} + \frac{20609148}{53} a - \frac{77673799}{53} \) |
\( \bigl[2 a^{5} + a^{4} - 11 a^{3} - 7 a^{2} + 6 a + 2\) , \( -2 a^{5} + a^{4} + 10 a^{3} - 2 a^{2} - 4 a - 1\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( a^{5} - 6 a^{4} - 3 a^{3} + 28 a^{2} - 4 a - 8\) , \( -4 a^{5} + 4 a^{4} + 18 a^{3} - 15 a^{2} - 4 a + 2\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-11a^{3}-7a^{2}+6a+2\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+6a+1\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+10a^{3}-2a^{2}-4a-1\right){x}^{2}+\left(a^{5}-6a^{4}-3a^{3}+28a^{2}-4a-8\right){x}-4a^{5}+4a^{4}+18a^{3}-15a^{2}-4a+2$ |
| 53.2-c1 |
53.2-c |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
53.2 |
\( 53 \) |
\( 53 \) |
$141.43156$ |
$(-2a^5+11a^3+3a^2-7a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$748.6889173$ |
0.658542 |
\( -\frac{53009648058}{53} a^{5} + \frac{19366168249}{53} a^{4} + \frac{306684080388}{53} a^{3} - \frac{60789537899}{53} a^{2} - \frac{272339497317}{53} a + \frac{112764452639}{53} \) |
\( \bigl[a^{5} - 5 a^{3} - a^{2} + 2 a\) , \( -a^{5} - a^{4} + 6 a^{3} + 7 a^{2} - 5 a - 4\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 3 a + 1\) , \( 5 a^{5} - 27 a^{3} - 6 a^{2} + 17 a\) , \( 2 a^{5} - 2 a^{4} - 8 a^{3} + 4 a^{2} + 4 a - 4\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-a^{2}+2a\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+3a+1\right){y}={x}^3+\left(-a^{5}-a^{4}+6a^{3}+7a^{2}-5a-4\right){x}^2+\left(5a^{5}-27a^{3}-6a^{2}+17a\right){x}+2a^{5}-2a^{4}-8a^{3}+4a^{2}+4a-4$ |
| 64.1-a1 |
64.1-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$143.67185$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1134.353802$ |
0.997769 |
\( 6428858220 a^{5} - \frac{26033067009}{2} a^{4} - 12199286286 a^{3} + \frac{36496947573}{2} a^{2} + \frac{3138647373}{2} a - 3169591470 \) |
\( \bigl[a^{5} - 6 a^{3} + 4 a - 2\) , \( -a^{5} - a^{4} + 6 a^{3} + 6 a^{2} - 4 a - 2\) , \( 2 a^{5} + a^{4} - 11 a^{3} - 7 a^{2} + 6 a + 3\) , \( 21 a^{5} + 18 a^{4} - 110 a^{3} - 118 a^{2} + 27 a + 28\) , \( 90 a^{5} + 73 a^{4} - 472 a^{3} - 485 a^{2} + 123 a + 106\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+4a-2\right){x}{y}+\left(2a^{5}+a^{4}-11a^{3}-7a^{2}+6a+3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+6a^{2}-4a-2\right){x}^{2}+\left(21a^{5}+18a^{4}-110a^{3}-118a^{2}+27a+28\right){x}+90a^{5}+73a^{4}-472a^{3}-485a^{2}+123a+106$ |
| 64.1-b1 |
64.1-b |
$4$ |
$21$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{42} \) |
$143.67185$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.3 |
$49$ |
\( 7 \) |
$15.86870131$ |
$0.141300615$ |
4.05894 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 1\) , \( a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 4 a + 3\) , \( -a^{5} - a^{4} + 6 a^{3} + 6 a^{2} - 4 a - 120\) , \( 39 a^{5} - 40 a^{4} - 234 a^{3} + 161 a^{2} + 235 a - 555\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-6a+1\right){x}^{2}+\left(-a^{5}-a^{4}+6a^{3}+6a^{2}-4a-120\right){x}+39a^{5}-40a^{4}-234a^{3}+161a^{2}+235a-555$ |
| 64.1-b2 |
64.1-b |
$4$ |
$21$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$143.67185$ |
$(2)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$0.755652443$ |
$149614.8855$ |
4.05894 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 5 a\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 6 a - 3\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 14 a^{2} - 8 a + 5\) , \( -2 a^{4} + 10 a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+5a\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+6a-3\right){x}^{2}+\left(-a^{5}+3a^{4}+6a^{3}-14a^{2}-8a+5\right){x}-2a^{4}+10a^{2}+2a-3$ |
| 64.1-b3 |
64.1-b |
$4$ |
$21$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{126} \) |
$143.67185$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.3 |
$49$ |
\( 3 \cdot 7 \) |
$5.289567106$ |
$1.271705543$ |
4.05894 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 5 a\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 6 a - 3\) , \( a^{4} - 5 a^{2} - a + 2\) , \( 9 a^{5} + 53 a^{4} - 54 a^{3} - 274 a^{2} - 8 a + 45\) , \( 166 a^{5} + 584 a^{4} - 996 a^{3} - 3086 a^{2} + 246 a + 583\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+5a\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+6a-3\right){x}^{2}+\left(9a^{5}+53a^{4}-54a^{3}-274a^{2}-8a+45\right){x}+166a^{5}+584a^{4}-996a^{3}-3086a^{2}+246a+583$ |
| 64.1-b4 |
64.1-b |
$4$ |
$21$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$143.67185$ |
$(2)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.1 |
$1$ |
\( 1 \) |
$2.266957331$ |
$16623.87616$ |
4.05894 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 1\) , \( a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 4 a + 3\) , \( -a^{5} - a^{4} + 6 a^{3} + 6 a^{2} - 4 a\) , \( -a^{5} + 6 a^{3} + a^{2} - 5 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-6a+1\right){x}^{2}+\left(-a^{5}-a^{4}+6a^{3}+6a^{2}-4a\right){x}-a^{5}+6a^{3}+a^{2}-5a-1$ |
| 64.1-c1 |
64.1-c |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$143.67185$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1134.353802$ |
0.997769 |
\( -108222819066 a^{5} - \frac{106843738041}{2} a^{4} + 622963051362 a^{3} + \frac{831474999369}{2} a^{2} - \frac{888201450783}{2} a - 219227741532 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 2\) , \( -2 a^{5} - a^{4} + 11 a^{3} + 8 a^{2} - 7 a - 4\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( -2 a^{3} + 5 a^{2} + 16 a - 4\) , \( 19 a^{5} - 9 a^{4} - 116 a^{3} + 35 a^{2} + 125 a - 58\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+2\right){x}{y}+\left(-a^{3}+a^{2}+3a-2\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+11a^{3}+8a^{2}-7a-4\right){x}^{2}+\left(-2a^{3}+5a^{2}+16a-4\right){x}+19a^{5}-9a^{4}-116a^{3}+35a^{2}+125a-58$ |
| 73.1-a1 |
73.1-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.1 |
\( 73 \) |
\( 73 \) |
$145.25584$ |
$(-a^4+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.156593084$ |
$4991.907210$ |
4.12546 |
\( -\frac{7944881364486114}{73} a^{5} + \frac{3436481017711149}{73} a^{4} + \frac{46182874076032257}{73} a^{3} - \frac{12031070663370121}{73} a^{2} - \frac{42465378916779911}{73} a + \frac{18367982817169226}{73} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a - 1\) , \( -a^{5} + 5 a^{3} + 2 a^{2} - a - 2\) , \( a^{5} - 6 a^{4} + 6 a^{3} + 8 a^{2} - 6 a\) , \( -37 a^{5} + 19 a^{4} + 137 a^{3} + 55 a^{2} - 31 a - 15\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(-a^{5}+5a^{3}+2a^{2}-a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a-1\right){x}^{2}+\left(a^{5}-6a^{4}+6a^{3}+8a^{2}-6a\right){x}-37a^{5}+19a^{4}+137a^{3}+55a^{2}-31a-15$ |
| 73.1-b1 |
73.1-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.1 |
\( 73 \) |
\( - 73^{3} \) |
$145.25584$ |
$(-a^4+6a^2+a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.096597477$ |
$23256.59122$ |
3.95206 |
\( \frac{326036037010734}{389017} a^{5} - \frac{141023570474088}{389017} a^{4} - \frac{1895217566307201}{389017} a^{3} + \frac{493721769365379}{389017} a^{2} + \frac{1742661943723836}{389017} a - \frac{753770685099240}{389017} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 4 a + 2\) , \( -a^{5} - a^{4} + 4 a^{3} + 7 a^{2} + 2 a - 4\) , \( a^{4} - 5 a^{2} + 3\) , \( -3 a^{5} - 2 a^{4} + 17 a^{3} + 16 a^{2} - 9 a - 3\) , \( -3 a^{5} - a^{4} + 15 a^{3} + 8 a^{2} - 7 a - 1\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+4a+2\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+7a^{2}+2a-4\right){x}^{2}+\left(-3a^{5}-2a^{4}+17a^{3}+16a^{2}-9a-3\right){x}-3a^{5}-a^{4}+15a^{3}+8a^{2}-7a-1$ |
| 73.1-b2 |
73.1-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.1 |
\( 73 \) |
\( -73 \) |
$145.25584$ |
$(-a^4+6a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.289792433$ |
$2584.065691$ |
3.95206 |
\( -\frac{2987766}{73} a^{5} - \frac{1182519}{73} a^{4} + \frac{17878725}{73} a^{3} + \frac{11322666}{73} a^{2} - \frac{13120137}{73} a - \frac{6413391}{73} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 5 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( 2 a^{5} + a^{4} - 11 a^{3} - 7 a^{2} + 6 a + 3\) , \( -4 a^{5} - 2 a^{4} + 22 a^{3} + 16 a^{2} - 11 a - 4\) , \( -3 a^{2} - 3 a\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+5a+1\right){x}{y}+\left(2a^{5}+a^{4}-11a^{3}-7a^{2}+6a+3\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-7a^{2}-2a+3\right){x}^{2}+\left(-4a^{5}-2a^{4}+22a^{3}+16a^{2}-11a-4\right){x}-3a^{2}-3a$ |
| 73.2-a1 |
73.2-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( 73^{3} \) |
$145.25584$ |
$(-a^3+a^2+4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9570.971502$ |
2.10464 |
\( \frac{21659278911}{389017} a^{5} - \frac{32546481532}{389017} a^{4} - \frac{88194498660}{389017} a^{3} + \frac{122762183576}{389017} a^{2} - \frac{26992748867}{389017} a - \frac{4680290404}{389017} \) |
\( \bigl[a^{5} - 6 a^{3} + 5 a - 1\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 2 a^{2} + 5 a - 1\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 4 a\) , \( 3 a^{5} - 3 a^{4} - 14 a^{3} + 9 a^{2} + 6 a - 3\) , \( 3 a^{5} - 3 a^{4} - 12 a^{3} + 4 a^{2} + 4 a - 1\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+5a-1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+4a\right){y}={x}^{3}+\left(2a^{5}-a^{4}-10a^{3}+2a^{2}+5a-1\right){x}^{2}+\left(3a^{5}-3a^{4}-14a^{3}+9a^{2}+6a-3\right){x}+3a^{5}-3a^{4}-12a^{3}+4a^{2}+4a-1$ |
| 73.2-a2 |
73.2-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( - 73^{6} \) |
$145.25584$ |
$(-a^3+a^2+4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4785.485751$ |
2.10464 |
\( -\frac{320290912915565456097}{151334226289} a^{5} + \frac{138482634039794169449}{151334226289} a^{4} + \frac{1861796302253775419664}{151334226289} a^{3} - \frac{484710401011385252408}{151334226289} a^{2} - \frac{1711772598210100331805}{151334226289} a + \frac{740333694887895038664}{151334226289} \) |
\( \bigl[a^{5} - 6 a^{3} + 5 a - 1\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 2 a^{2} + 5 a - 1\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 4 a\) , \( 8 a^{5} - 13 a^{4} - 24 a^{3} + 19 a^{2} + a - 8\) , \( 35 a^{5} - 61 a^{4} - 90 a^{3} + 67 a^{2} + 21 a - 9\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+5a-1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+4a\right){y}={x}^{3}+\left(2a^{5}-a^{4}-10a^{3}+2a^{2}+5a-1\right){x}^{2}+\left(8a^{5}-13a^{4}-24a^{3}+19a^{2}+a-8\right){x}+35a^{5}-61a^{4}-90a^{3}+67a^{2}+21a-9$ |
| 73.2-b1 |
73.2-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( -73 \) |
$145.25584$ |
$(-a^3+a^2+4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.104180428$ |
$7942.119355$ |
4.36672 |
\( \frac{1028052}{73} a^{5} - \frac{372357}{73} a^{4} - \frac{6063093}{73} a^{3} + \frac{1330506}{73} a^{2} + \frac{5514318}{73} a - \frac{2199528}{73} \) |
\( \bigl[a^{2} - 1\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a + 1\) , \( a^{5} - 6 a^{3} + 4 a - 1\) , \( 2 a^{3} - a^{2} - 3 a + 2\) , \( a^{5} - a^{3}\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{5}-6a^{3}+4a-1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a+1\right){x}^{2}+\left(2a^{3}-a^{2}-3a+2\right){x}+a^{5}-a^{3}$ |
| 73.2-b2 |
73.2-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.2 |
\( 73 \) |
\( - 73^{3} \) |
$145.25584$ |
$(-a^3+a^2+4a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.034726809$ |
$71479.07419$ |
4.36672 |
\( -\frac{13581313974}{389017} a^{5} - \frac{17638443684}{389017} a^{4} + \frac{21593446506}{389017} a^{3} + \frac{21091871961}{389017} a^{2} - \frac{9450990450}{389017} a - \frac{5380414884}{389017} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -a^{5} - a^{4} + 4 a^{3} + 7 a^{2} + 2 a - 4\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 2\) , \( -5 a^{5} - 2 a^{4} + 29 a^{3} + 18 a^{2} - 21 a - 7\) , \( 7 a^{5} + 3 a^{4} - 41 a^{3} - 25 a^{2} + 30 a + 12\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+7a^{2}+2a-4\right){x}^{2}+\left(-5a^{5}-2a^{4}+29a^{3}+18a^{2}-21a-7\right){x}+7a^{5}+3a^{4}-41a^{3}-25a^{2}+30a+12$ |
| 73.3-a1 |
73.3-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.3 |
\( 73 \) |
\( 73 \) |
$145.25584$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.156593084$ |
$4991.907210$ |
4.12546 |
\( \frac{278094377458640}{73} a^{5} + \frac{642934078410659}{73} a^{4} - \frac{182152153867413}{73} a^{3} - \frac{699217830211445}{73} a^{2} + \frac{52028885520733}{73} a + \frac{120287070481859}{73} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 4 a + 3\) , \( -a^{5} - a^{4} + 5 a^{3} + 7 a^{2} - a - 5\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 3 a + 1\) , \( 7 a^{5} - 8 a^{4} - 41 a^{3} + 36 a^{2} + 42 a - 36\) , \( -57 a^{5} + 31 a^{4} + 333 a^{3} - 128 a^{2} - 320 a + 168\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+4a+3\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+3a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+5a^{3}+7a^{2}-a-5\right){x}^{2}+\left(7a^{5}-8a^{4}-41a^{3}+36a^{2}+42a-36\right){x}-57a^{5}+31a^{4}+333a^{3}-128a^{2}-320a+168$ |
| 73.3-b1 |
73.3-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.3 |
\( 73 \) |
\( - 73^{3} \) |
$145.25584$ |
$(a^3-3a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.096597477$ |
$23256.59122$ |
3.95206 |
\( -\frac{11414085728562}{389017} a^{5} - \frac{26383616468415}{389017} a^{4} + \frac{7485858614169}{389017} a^{3} + \frac{28692214064964}{389017} a^{2} - \frac{2145000370473}{389017} a - \frac{4932305307999}{389017} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 4 a + 2\) , \( 2 a^{5} - 10 a^{3} - 3 a^{2} + 4 a + 3\) , \( a^{5} + a^{4} - 6 a^{3} - 6 a^{2} + 5 a + 2\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 14 a^{2} + a - 3\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 7 a^{2} + 5 a\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+4a+2\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-6a^{2}+5a+2\right){y}={x}^{3}+\left(2a^{5}-10a^{3}-3a^{2}+4a+3\right){x}^{2}+\left(a^{5}-3a^{4}-4a^{3}+14a^{2}+a-3\right){x}+2a^{5}-2a^{4}-10a^{3}+7a^{2}+5a$ |
| 73.3-b2 |
73.3-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.3 |
\( 73 \) |
\( -73 \) |
$145.25584$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.289792433$ |
$2584.065691$ |
3.95206 |
\( -\frac{3336714}{73} a^{5} + \frac{1239786}{73} a^{4} + \frac{20068155}{73} a^{3} - \frac{5284521}{73} a^{2} - \frac{18559530}{73} a + \frac{8072568}{73} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 5 a + 1\) , \( -2 a^{5} + 10 a^{3} + 3 a^{2} - 4 a - 1\) , \( 2 a^{5} - 11 a^{3} - 2 a^{2} + 7 a\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 12 a^{2} + 10 a - 8\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 6 a^{2} + 15 a - 9\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+5a+1\right){x}{y}+\left(2a^{5}-11a^{3}-2a^{2}+7a\right){y}={x}^{3}+\left(-2a^{5}+10a^{3}+3a^{2}-4a-1\right){x}^{2}+\left(a^{5}-2a^{4}-7a^{3}+12a^{2}+10a-8\right){x}+2a^{5}-a^{4}-13a^{3}+6a^{2}+15a-9$ |
| 73.4-a1 |
73.4-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.4 |
\( 73 \) |
\( 73^{3} \) |
$145.25584$ |
$(-2a^5-a^4+11a^3+8a^2-5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9570.971502$ |
2.10464 |
\( -\frac{61072144971}{389017} a^{5} - \frac{50857426705}{389017} a^{4} + \frac{324671695020}{389017} a^{3} + \frac{333670223669}{389017} a^{2} - \frac{86667673196}{389017} a - \frac{72784786636}{389017} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 4 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} - 2 a\) , \( a^{5} - 6 a^{3} + 4 a - 1\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 26 a^{2} - 6 a - 8\) , \( -11 a^{5} - 13 a^{4} + 68 a^{3} + 80 a^{2} - 56 a - 39\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+4a+1\right){x}{y}+\left(a^{5}-6a^{3}+4a-1\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}-2a\right){x}^{2}+\left(2a^{5}-6a^{4}-6a^{3}+26a^{2}-6a-8\right){x}-11a^{5}-13a^{4}+68a^{3}+80a^{2}-56a-39$ |
| 73.4-a2 |
73.4-a |
$2$ |
$2$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.4 |
\( 73 \) |
\( - 73^{6} \) |
$145.25584$ |
$(-2a^5-a^4+11a^3+8a^2-5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4785.485751$ |
2.10464 |
\( \frac{11239538114617327282}{151334226289} a^{5} + \frac{25894490311814308189}{151334226289} a^{4} - \frac{7488053448086646774}{151334226289} a^{3} - \frac{28123845945709006967}{151334226289} a^{2} + \frac{2138599853751210092}{151334226289} a + \frac{4855657280398554186}{151334226289} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( -3 a^{5} - a^{4} + 16 a^{3} + 9 a^{2} - 8 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 2 a + 1\) , \( -119 a^{5} + 116 a^{4} + 563 a^{3} - 404 a^{2} - 133 a + 55\) , \( -1046 a^{5} + 1189 a^{4} + 4833 a^{3} - 4390 a^{2} - 837 a + 790\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+6a+1\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-3a^{5}-a^{4}+16a^{3}+9a^{2}-8a-4\right){x}^{2}+\left(-119a^{5}+116a^{4}+563a^{3}-404a^{2}-133a+55\right){x}-1046a^{5}+1189a^{4}+4833a^{3}-4390a^{2}-837a+790$ |
| 73.4-b1 |
73.4-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.4 |
\( 73 \) |
\( - 73^{3} \) |
$145.25584$ |
$(-2a^5-a^4+11a^3+8a^2-5a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.034726809$ |
$71479.07419$ |
4.36672 |
\( \frac{304968174318}{389017} a^{5} - \frac{98320104117}{389017} a^{4} - \frac{1769914608570}{389017} a^{3} + \frac{267314006700}{389017} a^{2} + \frac{1582343839971}{389017} a - \frac{549364814820}{389017} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( 2 a^{5} - 10 a^{3} - 3 a^{2} + 4 a + 3\) , \( 2 a^{5} - 11 a^{3} - 2 a^{2} + 6 a\) , \( 3 a^{5} - 2 a^{4} - 13 a^{3} + 5 a^{2} + a + 1\) , \( a^{5} - 6 a^{3} + 2 a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(2a^{5}-11a^{3}-2a^{2}+6a\right){y}={x}^{3}+\left(2a^{5}-10a^{3}-3a^{2}+4a+3\right){x}^{2}+\left(3a^{5}-2a^{4}-13a^{3}+5a^{2}+a+1\right){x}+a^{5}-6a^{3}+2a^{2}+2a-1$ |
| 73.4-b2 |
73.4-b |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
73.4 |
\( 73 \) |
\( -73 \) |
$145.25584$ |
$(-2a^5-a^4+11a^3+8a^2-5a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.104180428$ |
$7942.119355$ |
4.36672 |
\( \frac{395037}{73} a^{5} + \frac{124416}{73} a^{4} - \frac{2475441}{73} a^{3} - \frac{1513890}{73} a^{2} + \frac{1849068}{73} a + \frac{886329}{73} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 6 a\) , \( -a^{5} + 6 a^{3} + 2 a^{2} - 5 a - 1\) , \( a^{5} - 5 a^{3} - a^{2} + 2 a + 1\) , \( -a^{5} - a^{4} + 7 a^{3} + 7 a^{2} - 7 a - 1\) , \( -2 a^{5} + 2 a^{4} + 10 a^{3} - 7 a^{2} - 4 a + 2\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+6a\right){x}{y}+\left(a^{5}-5a^{3}-a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+2a^{2}-5a-1\right){x}^{2}+\left(-a^{5}-a^{4}+7a^{3}+7a^{2}-7a-1\right){x}-2a^{5}+2a^{4}+10a^{3}-7a^{2}-4a+2$ |
| 81.1-a1 |
81.1-a |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{18} \) |
$146.52007$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7Ns |
$49$ |
\( 2 \) |
$1$ |
$33.76311985$ |
2.91039 |
\( 542387511 a^{5} + 1561871172 a^{4} - 3254325066 a^{3} - 8351743371 a^{2} + 1150066383 a + 1750311699 \) |
\( \bigl[a^{4} - 4 a^{2} - 2 a\) , \( -a^{5} - a^{4} + 6 a^{3} + 7 a^{2} - 5 a - 3\) , \( a^{5} - 5 a^{3} - a^{2} + 2 a + 1\) , \( 34 a^{5} - 25 a^{4} - 200 a^{3} + 113 a^{2} + 197 a - 126\) , \( 210 a^{5} - 105 a^{4} - 1224 a^{3} + 402 a^{2} + 1145 a - 558\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-2a\right){x}{y}+\left(a^{5}-5a^{3}-a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+7a^{2}-5a-3\right){x}^{2}+\left(34a^{5}-25a^{4}-200a^{3}+113a^{2}+197a-126\right){x}+210a^{5}-105a^{4}-1224a^{3}+402a^{2}+1145a-558$ |
| 81.1-b1 |
81.1-b |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{30} \) |
$146.52007$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1444.936651$ |
2.54191 |
\( -\frac{182007487}{9} a^{5} + \frac{291777437}{27} a^{4} + \frac{364014974}{3} a^{3} - \frac{912864724}{27} a^{2} - \frac{3021889742}{27} a + \frac{1318762211}{27} \) |
\( \bigl[a + 1\) , \( -a^{4} + 6 a^{2} - 3\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 3 a + 1\) , \( -a^{5} - a^{4} + 8 a^{3} - a^{2} - 6 a - 1\) , \( -4 a^{5} + 19 a^{4} - 57 a^{2} + 9 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+3a+1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-3\right){x}^{2}+\left(-a^{5}-a^{4}+8a^{3}-a^{2}-6a-1\right){x}-4a^{5}+19a^{4}-57a^{2}+9a+14$ |
| 81.1-c1 |
81.1-c |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$146.52007$ |
$(-a^4+5a^2+a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$7$ |
7Ns |
$1$ |
\( 2 \) |
$0.000632416$ |
$163321.2905$ |
6.54124 |
\( 542387511 a^{5} + 1561871172 a^{4} - 3254325066 a^{3} - 8351743371 a^{2} + 1150066383 a + 1750311699 \) |
\( \bigl[-a^{3} + a^{2} + 4 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( 8 a^{5} + 14 a^{4} - 40 a^{3} - 77 a^{2} - 12 a + 4\) , \( -39 a^{5} - 38 a^{4} + 197 a^{3} + 237 a^{2} - 5 a - 30\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+a-1\right){x}^{2}+\left(8a^{5}+14a^{4}-40a^{3}-77a^{2}-12a+4\right){x}-39a^{5}-38a^{4}+197a^{3}+237a^{2}-5a-30$ |
| 109.2-a1 |
109.2-a |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.2 |
\( 109 \) |
\( 109 \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.028427271$ |
$228021.3598$ |
3.80103 |
\( \frac{226035237834}{109} a^{5} - \frac{97631187426}{109} a^{4} - \frac{1313973773478}{109} a^{3} + \frac{341491987818}{109} a^{2} + \frac{1208131481781}{109} a - \frac{522043906923}{109} \) |
\( \bigl[-a^{3} + a^{2} + 3 a - 1\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 3 a + 1\) , \( a^{5} - 5 a^{3} - a^{2} + 2 a\) , \( -12 a^{5} - 17 a^{4} + 26 a^{3} + 37 a^{2} - 13 a - 17\) , \( 76 a^{5} + 181 a^{4} - 66 a^{3} - 217 a^{2} + 29 a + 48\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+3a-1\right){x}{y}+\left(a^{5}-5a^{3}-a^{2}+2a\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+3a+1\right){x}^{2}+\left(-12a^{5}-17a^{4}+26a^{3}+37a^{2}-13a-17\right){x}+76a^{5}+181a^{4}-66a^{3}-217a^{2}+29a+48$ |
| 109.2-a2 |
109.2-a |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.2 |
\( 109 \) |
\( 109^{3} \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.009475757$ |
$25335.70665$ |
3.80103 |
\( \frac{1841048757}{1295029} a^{5} + \frac{990923949}{1295029} a^{4} - \frac{11668911678}{1295029} a^{3} - \frac{5762569878}{1295029} a^{2} + \frac{9738182799}{1295029} a + \frac{2583242793}{1295029} \) |
\( \bigl[a^{2} - a - 1\) , \( 0\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 3 a\) , \( 40 a^{5} - 49 a^{4} - 183 a^{3} + 186 a^{2} + 26 a - 36\) , \( 1502 a^{5} - 1786 a^{4} - 6890 a^{3} + 6692 a^{2} + 1062 a - 1265\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-3a\right){y}={x}^{3}+\left(40a^{5}-49a^{4}-183a^{3}+186a^{2}+26a-36\right){x}+1502a^{5}-1786a^{4}-6890a^{3}+6692a^{2}+1062a-1265$ |
| 109.2-b1 |
109.2-b |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.2 |
\( 109 \) |
\( -109 \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.157754614$ |
$6061.263290$ |
5.04636 |
\( \frac{8533331774}{109} a^{5} - \frac{10142864642}{109} a^{4} - \frac{39144038834}{109} a^{3} + \frac{37993980604}{109} a^{2} + \frac{6039841516}{109} a - \frac{7179201885}{109} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 2 a^{2} + 6 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 2 a + 1\) , \( 0\) , \( 7 a^{5} - 7 a^{4} - 33 a^{3} + 25 a^{2} + 7 a - 2\) , \( 8 a^{5} - 9 a^{4} - 37 a^{3} + 33 a^{2} + 6 a - 5\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-2a^{2}+6a+1\right){x}{y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+2a+1\right){x}^{2}+\left(7a^{5}-7a^{4}-33a^{3}+25a^{2}+7a-2\right){x}+8a^{5}-9a^{4}-37a^{3}+33a^{2}+6a-5$ |
| 109.2-c1 |
109.2-c |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.2 |
\( 109 \) |
\( - 109^{5} \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2576.547694$ |
2.26632 |
\( \frac{117775584852408}{15386239549} a^{5} - \frac{111043020456715}{15386239549} a^{4} - \frac{594396981152429}{15386239549} a^{3} + \frac{382712496454367}{15386239549} a^{2} + \frac{250861683702408}{15386239549} a - \frac{118866578084812}{15386239549} \) |
\( \bigl[a^{2} - 2\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 7 a - 1\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + a + 2\) , \( a^{5} - 8 a^{3} - 4 a^{2} + 8 a + 3\) , \( 2 a^{5} + 2 a^{4} - 8 a^{3} - 6 a^{2} + 5 a + 2\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+3a^{2}+7a-1\right){x}^{2}+\left(a^{5}-8a^{3}-4a^{2}+8a+3\right){x}+2a^{5}+2a^{4}-8a^{3}-6a^{2}+5a+2$ |
| 109.3-a1 |
109.3-a |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.3 |
\( 109 \) |
\( 109 \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.028427271$ |
$228021.3598$ |
3.80103 |
\( -\frac{7714788507}{109} a^{5} - \frac{18259898904}{109} a^{4} + \frac{4051077516}{109} a^{3} + \frac{19642994505}{109} a^{2} - \frac{638148816}{109} a - \frac{3578522265}{109} \) |
\( \bigl[a^{5} - 6 a^{3} + 5 a - 2\) , \( 2 a^{5} + a^{4} - 11 a^{3} - 8 a^{2} + 5 a + 3\) , \( a^{5} - 6 a^{3} - a^{2} + 5 a\) , \( 3 a^{5} - 8 a^{4} - 5 a^{3} + 16 a^{2} + 9 a - 10\) , \( -13 a^{5} + 27 a^{4} + 22 a^{3} - 34 a^{2} - 5 a + 7\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+5a-2\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+5a\right){y}={x}^{3}+\left(2a^{5}+a^{4}-11a^{3}-8a^{2}+5a+3\right){x}^{2}+\left(3a^{5}-8a^{4}-5a^{3}+16a^{2}+9a-10\right){x}-13a^{5}+27a^{4}+22a^{3}-34a^{2}-5a+7$ |
| 109.3-a2 |
109.3-a |
$2$ |
$3$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.3 |
\( 109 \) |
\( 109^{3} \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.009475757$ |
$25335.70665$ |
3.80103 |
\( \frac{4052900610}{1295029} a^{5} + \frac{2024022573}{1295029} a^{4} - \frac{23694784524}{1295029} a^{3} - \frac{15206112099}{1295029} a^{2} + \frac{16716617514}{1295029} a + \frac{8159215401}{1295029} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( 2 a^{5} + a^{4} - 11 a^{3} - 7 a^{2} + 6 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 2\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 3 a\) , \( -2 a^{5} - 4 a^{4} + 11 a^{3} + 23 a^{2} - 3 a - 5\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+2\right){y}={x}^{3}+\left(2a^{5}+a^{4}-11a^{3}-7a^{2}+6a+3\right){x}^{2}+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+3a\right){x}-2a^{5}-4a^{4}+11a^{3}+23a^{2}-3a-5$ |
| 109.3-b1 |
109.3-b |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.3 |
\( 109 \) |
\( -109 \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.157754614$ |
$6061.263290$ |
5.04636 |
\( -\frac{17032697090}{109} a^{5} - \frac{14329875474}{109} a^{4} + \frac{90140230730}{109} a^{3} + \frac{92869085292}{109} a^{2} - \frac{24063927980}{109} a - \frac{20245315067}{109} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 2 a^{2} + 6 a\) , \( -a^{5} + a^{4} + 4 a^{3} - 3 a^{2}\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + a + 2\) , \( a^{5} + 2 a^{4} - 6 a^{3} - 8 a^{2} + 2\) , \( a^{5} + 2 a^{4} - 7 a^{3} - 10 a^{2} + 2 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-2a^{2}+6a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+a+2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-3a^{2}\right){x}^{2}+\left(a^{5}+2a^{4}-6a^{3}-8a^{2}+2\right){x}+a^{5}+2a^{4}-7a^{3}-10a^{2}+2a+2$ |
| 109.3-c1 |
109.3-c |
$1$ |
$1$ |
6.6.1292517.1 |
$6$ |
$[6, 0]$ |
109.3 |
\( 109 \) |
\( - 109^{5} \) |
$150.19042$ |
$(a^5-6a^3-a^2+7a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2576.547694$ |
2.26632 |
\( -\frac{106704321903359}{15386239549} a^{5} - \frac{165770041433515}{15386239549} a^{4} + \frac{527969403458135}{15386239549} a^{3} + \frac{990281550047734}{15386239549} a^{2} + \frac{81307692933067}{15386239549} a - \frac{334972175983593}{15386239549} \) |
\( \bigl[-a^{3} + a^{2} + 4 a - 2\) , \( -a^{3} + 3 a + 1\) , \( a^{5} - 6 a^{3} + 4 a - 2\) , \( a^{5} - 6 a^{3} + 2 a^{2} + 3 a - 3\) , \( -4 a^{5} - 2 a^{4} + 22 a^{3} + 17 a^{2} - 15 a - 10\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{5}-6a^{3}+4a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(a^{5}-6a^{3}+2a^{2}+3a-3\right){x}-4a^{5}-2a^{4}+22a^{3}+17a^{2}-15a-10$ |
*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.
