| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$2$ |
$3$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$126.21867$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17242.32995$ |
1.35634 |
\( -713527881 a^{5} + 2330801731 a^{4} + 1329458751 a^{3} - 5965582626 a^{2} - 1007746483 a + 563755026 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 2 a - 2\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 5 a - 4\) , \( 3 a^{5} - 6 a^{4} - 23 a^{3} + 29 a^{2} + 48 a - 12\) , \( -11 a^{5} + 27 a^{4} + 53 a^{3} - 88 a^{2} - 91 a + 25\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+5a-4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-2a-2\right){x}^{2}+\left(3a^{5}-6a^{4}-23a^{3}+29a^{2}+48a-12\right){x}-11a^{5}+27a^{4}+53a^{3}-88a^{2}-91a+25$ |
| 1.1-a2 |
1.1-a |
$2$ |
$3$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$126.21867$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$23.65203011$ |
1.35634 |
\( -3173411505733159920311156467 a^{5} + 10365486659128555248808418347 a^{4} + 5914089315880839869937229951 a^{3} - 26529802106967835674458663364 a^{2} - 4484806235806003425212549021 a + 2505942638562922589671094273 \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 15 a^{2} + 6 a - 1\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 8 a - 4\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 6 a^{2} + 12 a + 1\) , \( -391 a^{5} + 1119 a^{4} + 1209 a^{3} - 2867 a^{2} - 1777 a - 189\) , \( -4865 a^{5} + 14454 a^{4} + 13409 a^{3} - 36931 a^{2} - 17984 a - 904\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+15a^{2}+6a-1\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+6a^{2}+12a+1\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+8a-4\right){x}^{2}+\left(-391a^{5}+1119a^{4}+1209a^{3}-2867a^{2}-1777a-189\right){x}-4865a^{5}+14454a^{4}+13409a^{3}-36931a^{2}-17984a-904$ |
| 1.1-b1 |
1.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$126.21867$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$1558.674666$ |
1.10350 |
\( 69618230 a^{5} + 90964008 a^{4} - 1295258299 a^{3} + 451586144 a^{2} + 2806547659 a - 684726662 \) |
\( \bigl[3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 17 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a + 1\) , \( 8 a^{5} - 21 a^{4} - 37 a^{3} + 71 a^{2} + 65 a - 27\) , \( 103 a^{5} - 247 a^{4} - 519 a^{3} + 825 a^{2} + 903 a - 265\bigr] \) |
${y}^2+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+17a-3\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(8a^{5}-21a^{4}-37a^{3}+71a^{2}+65a-27\right){x}+103a^{5}-247a^{4}-519a^{3}+825a^{2}+903a-265$ |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{5} \) |
$161.31933$ |
$(-a^5+3a^4+3a^3-8a^2-4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$2389.584451$ |
1.69176 |
\( \frac{3060882007902}{2476099} a^{5} + \frac{169186045836}{2476099} a^{4} - \frac{18314501541423}{2476099} a^{3} - \frac{18922602739972}{2476099} a^{2} - \frac{839199870487}{2476099} a + \frac{1545839548872}{2476099} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 12 a - 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 4 a^{2} - 8 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + a - 1\) , \( -2 a^{5} + 7 a^{4} + 4 a^{3} - 17 a^{2} + a + 6\) , \( -3 a^{5} + 9 a^{4} + 8 a^{3} - 22 a^{2} - 8 a + 1\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+12a-1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-4a^{2}-8a-3\right){x}^{2}+\left(-2a^{5}+7a^{4}+4a^{3}-17a^{2}+a+6\right){x}-3a^{5}+9a^{4}+8a^{3}-22a^{2}-8a+1$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$161.31933$ |
$(a^5-3a^4-2a^3+6a^2+2a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.027761103$ |
$11174.45158$ |
3.95322 |
\( \frac{104511465878}{6859} a^{5} - \frac{355185723017}{6859} a^{4} - \frac{129840597431}{6859} a^{3} + \frac{42439885805}{361} a^{2} + \frac{128793896473}{6859} a - \frac{74924952655}{6859} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 3\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 3 a - 3\) , \( 3 a^{5} - 9 a^{4} - 8 a^{3} + 24 a^{2} + 11 a - 4\) , \( 2 a^{5} - 6 a^{4} - 7 a^{3} + 18 a^{2} + 10 a - 7\) , \( 3 a^{5} - 5 a^{4} - 21 a^{3} + 12 a^{2} + 40 a + 8\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-3\right){x}{y}+\left(3a^{5}-9a^{4}-8a^{3}+24a^{2}+11a-4\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+3a-3\right){x}^{2}+\left(2a^{5}-6a^{4}-7a^{3}+18a^{2}+10a-7\right){x}+3a^{5}-5a^{4}-21a^{3}+12a^{2}+40a+8$ |
| 19.2-b1 |
19.2-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{5} \) |
$161.31933$ |
$(a^5-3a^4-2a^3+6a^2+2a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3568.665676$ |
2.52651 |
\( \frac{154290262488}{2476099} a^{5} - \frac{397003569817}{2476099} a^{4} - \frac{679028411834}{2476099} a^{3} + \frac{65900307920}{130321} a^{2} + \frac{1119158324839}{2476099} a - \frac{353903502980}{2476099} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + a\) , \( -2 a^{5} + 6 a^{4} + 5 a^{3} - 16 a^{2} - 4 a + 4\) , \( a + 1\) , \( -13 a^{5} + 41 a^{4} + 26 a^{3} - 103 a^{2} - 18 a + 11\) , \( -20 a^{5} + 65 a^{4} + 37 a^{3} - 165 a^{2} - 26 a + 15\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+5a^{3}-16a^{2}-4a+4\right){x}^{2}+\left(-13a^{5}+41a^{4}+26a^{3}-103a^{2}-18a+11\right){x}-20a^{5}+65a^{4}+37a^{3}-165a^{2}-26a+15$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$167.10526$ |
$(-a^5+3a^4+3a^3-9a^2-3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.192463485$ |
$5144.822769$ |
4.20615 |
\( \frac{61976992282}{29} a^{5} - \frac{202542789178}{29} a^{4} - \frac{115218820510}{29} a^{3} + \frac{518404711161}{29} a^{2} + \frac{86880823374}{29} a - \frac{49246406795}{29} \) |
\( \bigl[a^{4} - 3 a^{3} - 2 a^{2} + 7 a + 2\) , \( -2 a^{5} + 6 a^{4} + 6 a^{3} - 17 a^{2} - 10 a + 3\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 14 a^{2} + 13 a - 2\) , \( -10 a^{5} + 26 a^{4} + 49 a^{3} - 90 a^{2} - 96 a + 24\) , \( -15 a^{5} + 41 a^{4} + 74 a^{3} - 150 a^{2} - 155 a + 40\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-2a^{2}+7a+2\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+14a^{2}+13a-2\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+6a^{3}-17a^{2}-10a+3\right){x}^{2}+\left(-10a^{5}+26a^{4}+49a^{3}-90a^{2}-96a+24\right){x}-15a^{5}+41a^{4}+74a^{3}-150a^{2}-155a+40$ |
| 29.1-b1 |
29.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$167.10526$ |
$(-a^5+3a^4+3a^3-9a^2-3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.049340695$ |
$9876.532820$ |
4.14005 |
\( \frac{2571851403}{841} a^{5} - \frac{4510344844}{841} a^{4} - \frac{16503656131}{841} a^{3} + \frac{11403509029}{841} a^{2} + \frac{33542390179}{841} a + \frac{10650168305}{841} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 11 a - 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 6 a^{2} - 2 a - 2\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 9 a - 4\) , \( 2 a^{5} - 6 a^{4} - 9 a^{3} + 22 a^{2} + 20 a - 4\) , \( -a^{4} - a^{3} + 8 a^{2} + 9 a - 3\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+11a-1\right){x}{y}+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+9a-4\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-6a^{2}-2a-2\right){x}^{2}+\left(2a^{5}-6a^{4}-9a^{3}+22a^{2}+20a-4\right){x}-a^{4}-a^{3}+8a^{2}+9a-3$ |
| 29.1-c1 |
29.1-c |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$167.10526$ |
$(-a^5+3a^4+3a^3-9a^2-3a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.002540538$ |
$45895.12290$ |
5.94347 |
\( \frac{119047546}{841} a^{5} - \frac{327933136}{841} a^{4} - \frac{433153031}{841} a^{3} + \frac{925906681}{841} a^{2} + \frac{727943423}{841} a - \frac{211904273}{841} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 9 a + 1\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 8 a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a\) , \( -3 a^{4} + 10 a^{3} + 7 a^{2} - 26 a - 10\) , \( -3 a^{5} + 4 a^{4} + 24 a^{3} - 10 a^{2} - 53 a - 20\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+9a+1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+8a-3\right){x}^{2}+\left(-3a^{4}+10a^{3}+7a^{2}-26a-10\right){x}-3a^{5}+4a^{4}+24a^{3}-10a^{2}-53a-20$ |
| 29.3-a1 |
29.3-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$167.10526$ |
$(a^5-3a^4-2a^3+6a^2+2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.011995461$ |
$39799.78872$ |
4.05596 |
\( \frac{221032}{841} a^{5} - \frac{572323}{841} a^{4} - \frac{471666}{841} a^{3} + \frac{538596}{841} a^{2} + \frac{1044032}{841} a + \frac{1641230}{841} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( a^{4} - 4 a^{3} + 11 a\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 14 a^{2} + 12 a - 2\) , \( 10 a^{5} - 35 a^{4} - 8 a^{3} + 76 a^{2} + 9 a - 4\) , \( -38 a^{5} + 132 a^{4} + 37 a^{3} - 288 a^{2} - 34 a + 24\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a-1\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+14a^{2}+12a-2\right){y}={x}^{3}+\left(a^{4}-4a^{3}+11a\right){x}^{2}+\left(10a^{5}-35a^{4}-8a^{3}+76a^{2}+9a-4\right){x}-38a^{5}+132a^{4}+37a^{3}-288a^{2}-34a+24$ |
| 29.4-a1 |
29.4-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( -29 \) |
$167.10526$ |
$(a^2-2a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.031859521$ |
$33534.53151$ |
4.53835 |
\( -\frac{59344551490}{29} a^{5} + \frac{193842145260}{29} a^{4} + \frac{110594651472}{29} a^{3} - \frac{496130265845}{29} a^{2} - \frac{83869480840}{29} a + \frac{46863333382}{29} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 6 a - 4\) , \( -3 a^{5} + 10 a^{4} + 5 a^{3} - 26 a^{2} - 2 a + 7\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 11 a - 2\) , \( a^{5} - 8 a^{3} - a^{2} + 15 a + 10\) , \( 8 a^{5} - 22 a^{4} - 21 a^{3} + 55 a^{2} + 23 a + 1\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+6a-4\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+11a-2\right){y}={x}^{3}+\left(-3a^{5}+10a^{4}+5a^{3}-26a^{2}-2a+7\right){x}^{2}+\left(a^{5}-8a^{3}-a^{2}+15a+10\right){x}+8a^{5}-22a^{4}-21a^{3}+55a^{2}+23a+1$ |
| 29.4-b1 |
29.4-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{7} \) |
$167.10526$ |
$(a^2-2a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.021285924$ |
$6125.751144$ |
3.87718 |
\( -\frac{10576501772888}{17249876309} a^{5} + \frac{30684107325722}{17249876309} a^{4} + \frac{9550311934666}{17249876309} a^{3} - \frac{81605087560838}{17249876309} a^{2} + \frac{10063286377715}{17249876309} a + \frac{16583497932006}{17249876309} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 11 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 1\) , \( -3 a^{5} + 10 a^{4} + 3 a^{3} - 21 a^{2} - a\) , \( -85 a^{5} + 291 a^{4} + 94 a^{3} - 640 a^{2} - 105 a + 58\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+11a-1\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+8a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(-3a^{5}+10a^{4}+3a^{3}-21a^{2}-a\right){x}-85a^{5}+291a^{4}+94a^{3}-640a^{2}-105a+58$ |
| 29.4-c1 |
29.4-c |
$2$ |
$3$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( -29 \) |
$167.10526$ |
$(a^2-2a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$3.957552147$ |
$3.130098427$ |
4.26222 |
\( -\frac{61552291988378339328827}{29} a^{5} + \frac{108272845536099489867930}{29} a^{4} + \frac{395403349463381380906095}{29} a^{3} - \frac{274036730257245363907994}{29} a^{2} - \frac{804659831415094141348378}{29} a - \frac{255444408231731420144507}{29} \) |
\( \bigl[3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 18 a - 4\) , \( a - 1\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 13 a\) , \( -123 a^{5} + 238 a^{4} + 731 a^{3} - 616 a^{2} - 1451 a - 429\) , \( -1172 a^{5} + 2094 a^{4} + 7429 a^{3} - 5284 a^{2} - 15069 a - 4833\bigr] \) |
${y}^2+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+18a-4\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+13a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-123a^{5}+238a^{4}+731a^{3}-616a^{2}-1451a-429\right){x}-1172a^{5}+2094a^{4}+7429a^{3}-5284a^{2}-15069a-4833$ |
| 29.4-c2 |
29.4-c |
$2$ |
$3$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( - 29^{3} \) |
$167.10526$ |
$(a^2-2a-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1.319184049$ |
$2281.841753$ |
4.26222 |
\( -\frac{82192901373}{24389} a^{5} + \frac{144662698959}{24389} a^{4} + \frac{527819385489}{24389} a^{3} - \frac{366387022826}{24389} a^{2} - \frac{1073950996279}{24389} a - \frac{340260108707}{24389} \) |
\( \bigl[3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 18 a - 4\) , \( a - 1\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 13 a\) , \( -8 a^{5} + 18 a^{4} + 46 a^{3} - 61 a^{2} - 86 a + 11\) , \( -13 a^{5} + 31 a^{4} + 68 a^{3} - 101 a^{2} - 124 a + 20\bigr] \) |
${y}^2+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+18a-4\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+13a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a^{5}+18a^{4}+46a^{3}-61a^{2}-86a+11\right){x}-13a^{5}+31a^{4}+68a^{3}-101a^{2}-124a+20$ |
| 29.4-d1 |
29.4-d |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( -29 \) |
$167.10526$ |
$(a^2-2a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.110008654$ |
$6196.219824$ |
2.89548 |
\( \frac{27325969024}{29} a^{5} + \frac{647684577}{29} a^{4} - \frac{162682485456}{29} a^{3} - \frac{165372042432}{29} a^{2} - \frac{6831902917}{29} a + \frac{13499870339}{29} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 3\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 5 a - 4\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 6 a - 4\) , \( 13 a^{5} - 27 a^{4} - 71 a^{3} + 71 a^{2} + 137 a + 32\) , \( -2 a^{5} + 2 a^{4} + 18 a^{3} - 4 a^{2} - 40 a - 18\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-3\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+6a-4\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+5a-4\right){x}^{2}+\left(13a^{5}-27a^{4}-71a^{3}+71a^{2}+137a+32\right){x}-2a^{5}+2a^{4}+18a^{3}-4a^{2}-40a-18$ |
| 31.1-a1 |
31.1-a |
$2$ |
$2$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$168.03655$ |
$(a^4-3a^3-2a^2+6a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.225025563$ |
$18156.81499$ |
4.33888 |
\( -\frac{87545264}{31} a^{5} + \frac{209879216}{31} a^{4} + \frac{441715644}{31} a^{3} - \frac{700561221}{31} a^{2} - \frac{771424232}{31} a + \frac{218739400}{31} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 6 a^{2} + 12 a\) , \( -2 a^{5} + 6 a^{4} + 6 a^{3} - 17 a^{2} - 8 a + 5\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 11 a - 1\) , \( -2 a^{5} + 4 a^{4} + 14 a^{3} - 18 a^{2} - 25 a + 10\) , \( -2 a^{5} + 3 a^{4} + 17 a^{3} - 17 a^{2} - 31 a + 9\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+6a^{2}+12a\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+11a-1\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+6a^{3}-17a^{2}-8a+5\right){x}^{2}+\left(-2a^{5}+4a^{4}+14a^{3}-18a^{2}-25a+10\right){x}-2a^{5}+3a^{4}+17a^{3}-17a^{2}-31a+9$ |
| 31.1-a2 |
31.1-a |
$2$ |
$2$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$168.03655$ |
$(a^4-3a^3-2a^2+6a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.450051126$ |
$4539.203748$ |
4.33888 |
\( -\frac{34344634184443274}{961} a^{5} + \frac{82373974402444462}{961} a^{4} + \frac{173245745234180222}{961} a^{3} - \frac{275098133496983428}{961} a^{2} - \frac{302522387285559123}{961} a + \frac{86196558637461516}{961} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + a\) , \( -a^{5} + 4 a^{4} + a^{3} - 12 a^{2} - a + 3\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 6 a - 3\) , \( 48 a^{5} - 134 a^{4} - 174 a^{3} + 383 a^{2} + 298 a - 94\) , \( 107 a^{5} - 194 a^{4} - 785 a^{3} + 895 a^{2} + 1418 a - 389\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+a\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+6a-3\right){y}={x}^{3}+\left(-a^{5}+4a^{4}+a^{3}-12a^{2}-a+3\right){x}^{2}+\left(48a^{5}-134a^{4}-174a^{3}+383a^{2}+298a-94\right){x}+107a^{5}-194a^{4}-785a^{3}+895a^{2}+1418a-389$ |
| 31.1-b1 |
31.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$168.03655$ |
$(a^4-3a^3-2a^2+6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.027758431$ |
$19816.37743$ |
4.67321 |
\( -\frac{1080985496727333736}{961} a^{5} + \frac{3530881923672071080}{961} a^{4} + \frac{2014565243797253718}{961} a^{3} - \frac{9037067219580255040}{961} a^{2} - \frac{1527696836843885117}{961} a + \frac{853620088963124074}{961} \) |
\( \bigl[a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 2\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 8 a^{2} + 15 a - 1\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 5 a - 3\) , \( -53 a^{5} + 125 a^{4} + 272 a^{3} - 420 a^{2} - 472 a + 139\) , \( 178 a^{5} - 426 a^{4} - 903 a^{3} + 1428 a^{2} + 1582 a - 450\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-2a^{2}+8a+2\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+5a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-7a^{3}+8a^{2}+15a-1\right){x}^{2}+\left(-53a^{5}+125a^{4}+272a^{3}-420a^{2}-472a+139\right){x}+178a^{5}-426a^{4}-903a^{3}+1428a^{2}+1582a-450$ |
| 41.1-a1 |
41.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$171.99755$ |
$(-2a^5+7a^4+2a^3-17a^2+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1887.753650$ |
2.67295 |
\( \frac{184798533475517384}{2825761} a^{5} - \frac{634558190065260095}{2825761} a^{4} - \frac{198970959519225097}{2825761} a^{3} + \frac{1394070455930040405}{2825761} a^{2} + \frac{218784322148776513}{2825761} a - \frac{128888909798068725}{2825761} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 9 a\) , \( a^{5} - 4 a^{4} + a^{3} + 10 a^{2} - 7 a - 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 12 a - 1\) , \( 34 a^{5} - 89 a^{4} - 148 a^{3} + 298 a^{2} + 235 a - 128\) , \( 216 a^{5} - 521 a^{4} - 1075 a^{3} + 1737 a^{2} + 1861 a - 560\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+9a\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+12a-1\right){y}={x}^3+\left(a^{5}-4a^{4}+a^{3}+10a^{2}-7a-3\right){x}^2+\left(34a^{5}-89a^{4}-148a^{3}+298a^{2}+235a-128\right){x}+216a^{5}-521a^{4}-1075a^{3}+1737a^{2}+1861a-560$ |
| 41.1-b1 |
41.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$171.99755$ |
$(a^5-2a^4-5a^3+5a^2+9a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.020365394$ |
$12742.47021$ |
4.40933 |
\( \frac{94719397734}{2825761} a^{5} - \frac{97025680889}{2825761} a^{4} - \frac{530162705388}{2825761} a^{3} + \frac{185035609457}{2825761} a^{2} + \frac{869928260478}{2825761} a + \frac{288264461864}{2825761} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 9 a + 1\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 9 a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + a\) , \( -7 a^{5} + 25 a^{4} + 6 a^{3} - 50 a^{2} - 17 a + 7\) , \( 464 a^{5} - 1588 a^{4} - 518 a^{3} + 3512 a^{2} + 558 a - 326\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+9a+1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+a\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+9a-4\right){x}^{2}+\left(-7a^{5}+25a^{4}+6a^{3}-50a^{2}-17a+7\right){x}+464a^{5}-1588a^{4}-518a^{3}+3512a^{2}+558a-326$ |
| 41.1-c1 |
41.1-c |
$2$ |
$2$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$171.99755$ |
$(a^5-2a^4-5a^3+5a^2+9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.230108178$ |
$5601.760957$ |
4.10661 |
\( \frac{20098618120}{68921} a^{5} - \frac{68965883371}{68921} a^{4} - \frac{21836676825}{68921} a^{3} + \frac{151598668934}{68921} a^{2} + \frac{24227121743}{68921} a - \frac{13846394231}{68921} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 6 a^{2} + 12 a\) , \( -3 a^{5} + 10 a^{4} + 5 a^{3} - 26 a^{2} - 4 a + 6\) , \( a\) , \( -a^{5} + 3 a^{4} + 5 a^{3} - 13 a^{2} - 10 a + 13\) , \( -4 a^{5} + 11 a^{4} + 15 a^{3} - 34 a^{2} - 22 a + 12\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+6a^{2}+12a\right){x}{y}+a{y}={x}^{3}+\left(-3a^{5}+10a^{4}+5a^{3}-26a^{2}-4a+6\right){x}^{2}+\left(-a^{5}+3a^{4}+5a^{3}-13a^{2}-10a+13\right){x}-4a^{5}+11a^{4}+15a^{3}-34a^{2}-22a+12$ |
| 41.1-c2 |
41.1-c |
$2$ |
$2$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{6} \) |
$171.99755$ |
$(a^5-2a^4-5a^3+5a^2+9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.460216357$ |
$1400.440239$ |
4.10661 |
\( -\frac{1720806778240101458072}{4750104241} a^{5} + \frac{5908883813727589054585}{4750104241} a^{4} + \frac{1852764350296802013267}{4750104241} a^{3} - \frac{12981312354500157798535}{4750104241} a^{2} - \frac{2037256663398903848677}{4750104241} a + \frac{1200183770741073301968}{4750104241} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 6 a^{2} + 12 a\) , \( -3 a^{5} + 10 a^{4} + 5 a^{3} - 26 a^{2} - 4 a + 6\) , \( a\) , \( 9 a^{5} - 27 a^{4} - 25 a^{3} + 67 a^{2} + 45 a + 3\) , \( 22 a^{5} - 70 a^{4} - 42 a^{3} + 156 a^{2} + 69 a\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+6a^{2}+12a\right){x}{y}+a{y}={x}^{3}+\left(-3a^{5}+10a^{4}+5a^{3}-26a^{2}-4a+6\right){x}^{2}+\left(9a^{5}-27a^{4}-25a^{3}+67a^{2}+45a+3\right){x}+22a^{5}-70a^{4}-42a^{3}+156a^{2}+69a$ |
| 59.1-a1 |
59.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( -59 \) |
$177.29423$ |
$(a^4-3a^3-a^2+5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.092603735$ |
$12113.60321$ |
4.76505 |
\( \frac{133775718}{59} a^{5} - \frac{459379056}{59} a^{4} - \frac{143920993}{59} a^{3} + \frac{1009135256}{59} a^{2} + \frac{158104408}{59} a - \frac{93303846}{59} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + a - 1\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 8 a^{2} - 14 a + 1\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 15 a^{2} + 6 a - 2\) , \( -5 a^{5} + 13 a^{4} + 23 a^{3} - 43 a^{2} - 40 a + 13\) , \( -7 a^{5} + 17 a^{4} + 35 a^{3} - 57 a^{2} - 61 a + 17\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+a-1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+15a^{2}+6a-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+7a^{3}-8a^{2}-14a+1\right){x}^{2}+\left(-5a^{5}+13a^{4}+23a^{3}-43a^{2}-40a+13\right){x}-7a^{5}+17a^{4}+35a^{3}-57a^{2}-61a+17$ |
| 59.1-b1 |
59.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( 59^{2} \) |
$177.29423$ |
$(a^4-3a^3-a^2+5a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.002631181$ |
$49950.02714$ |
6.69937 |
\( \frac{4143724600}{3481} a^{5} - \frac{9932750475}{3481} a^{4} - \frac{20903785595}{3481} a^{3} + \frac{33168140562}{3481} a^{2} + \frac{36495637111}{3481} a - \frac{10386145739}{3481} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a\) , \( -a^{5} + 4 a^{4} + a^{3} - 12 a^{2} + 5\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 14 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 4 a^{2} + 6 a + 4\) , \( 3 a^{5} - 9 a^{4} - 7 a^{3} + 23 a^{2} + 7 a - 1\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+14a\right){y}={x}^{3}+\left(-a^{5}+4a^{4}+a^{3}-12a^{2}+5\right){x}^{2}+\left(a^{5}-2a^{4}-4a^{3}+4a^{2}+6a+4\right){x}+3a^{5}-9a^{4}-7a^{3}+23a^{2}+7a-1$ |
| 59.1-c1 |
59.1-c |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( 59 \) |
$177.29423$ |
$(a^4-3a^3-a^2+5a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.001733844$ |
$161852.3951$ |
7.15231 |
\( \frac{162403826}{59} a^{5} - \frac{28375087}{59} a^{4} - \frac{973465057}{59} a^{3} - \frac{792236698}{59} a^{2} + \frac{196155264}{59} a + \frac{144591309}{59} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 8 a^{3} + 14 a^{2} + 12 a - 2\) , \( -a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a\) , \( a^{5} + a^{4} - 7 a^{3} - 11 a^{2} - 4 a\) , \( -5 a^{5} + 2 a^{4} + 28 a^{3} + 21 a^{2} - 3 a - 2\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-8a^{3}+14a^{2}+12a-2\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a^{5}+a^{4}-7a^{3}-11a^{2}-4a\right){x}-5a^{5}+2a^{4}+28a^{3}+21a^{2}-3a-2$ |
| 59.1-d1 |
59.1-d |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( 59 \) |
$177.29423$ |
$(a^4-3a^3-a^2+5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.013765084$ |
$70647.66360$ |
4.13088 |
\( \frac{658047776}{59} a^{5} - \frac{1581319545}{59} a^{4} - \frac{3307585153}{59} a^{3} + \frac{5269830698}{59} a^{2} + \frac{5769317396}{59} a - \frac{1640359830}{59} \) |
\( \bigl[3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 18 a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + 6 a - 2\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 1\) , \( -9 a^{5} + 24 a^{4} + 36 a^{3} - 68 a^{2} - 63 a + 12\) , \( -10 a^{5} + 27 a^{4} + 41 a^{3} - 82 a^{2} - 69 a + 22\bigr] \) |
${y}^2+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+18a-4\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+8a+1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+6a-2\right){x}^{2}+\left(-9a^{5}+24a^{4}+36a^{3}-68a^{2}-63a+12\right){x}-10a^{5}+27a^{4}+41a^{3}-82a^{2}-69a+22$ |
| 61.1-a1 |
61.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
61.1 |
\( 61 \) |
\( 61 \) |
$177.78745$ |
$(a^5-3a^4-2a^3+8a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.021370380$ |
$44806.01130$ |
4.06738 |
\( -\frac{606993377224956}{61} a^{5} + \frac{1067724662759617}{61} a^{4} + \frac{3899240899057230}{61} a^{3} - \frac{2702392958253822}{61} a^{2} - \frac{7935093439652787}{61} a - \frac{2519046146716798}{61} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 12 a - 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 2\) , \( 13 a^{5} - 44 a^{4} - 18 a^{3} + 111 a^{2} + 2 a - 13\) , \( -32 a^{5} + 102 a^{4} + 69 a^{3} - 267 a^{2} - 67 a + 31\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+5a-1\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+8a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+12a-3\right){x}^{2}+\left(13a^{5}-44a^{4}-18a^{3}+111a^{2}+2a-13\right){x}-32a^{5}+102a^{4}+69a^{3}-267a^{2}-67a+31$ |
| 61.1-b1 |
61.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
61.1 |
\( 61 \) |
\( -61 \) |
$177.78745$ |
$(a^5-3a^4-2a^3+8a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$4494.607577$ |
3.18204 |
\( -\frac{3236211}{61} a^{5} + \frac{5843873}{61} a^{4} + \frac{20853170}{61} a^{3} - \frac{15284256}{61} a^{2} - \frac{43567600}{61} a - \frac{13782510}{61} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 3 a + 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 9 a - 3\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 6 a^{2} - 11 a - 3\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-9a^{2}-3a+2\right){x}^{2}+\left(-a^{4}+3a^{3}+3a^{2}-9a-3\right){x}-a^{5}+2a^{4}+6a^{3}-6a^{2}-11a-3$ |
| 61.3-a1 |
61.3-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
61.3 |
\( 61 \) |
\( - 61^{3} \) |
$177.78745$ |
$(a^5-3a^4-2a^3+7a^2+a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.015483435$ |
$23611.91056$ |
4.65893 |
\( \frac{117608856}{226981} a^{5} - \frac{1352245392}{226981} a^{4} + \frac{2780287442}{226981} a^{3} + \frac{2955306808}{226981} a^{2} - \frac{6245864655}{226981} a - \frac{2748353492}{226981} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + 6 a - 1\) , \( -a^{4} + 4 a^{3} - 11 a + 2\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 7 a^{2} + 11 a - 1\) , \( -3 a^{5} + 5 a^{4} + 21 a^{3} - 16 a^{2} - 44 a - 1\) , \( -3 a^{5} + 5 a^{4} + 21 a^{3} - 16 a^{2} - 43 a - 4\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+6a-1\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+7a^{2}+11a-1\right){y}={x}^{3}+\left(-a^{4}+4a^{3}-11a+2\right){x}^{2}+\left(-3a^{5}+5a^{4}+21a^{3}-16a^{2}-44a-1\right){x}-3a^{5}+5a^{4}+21a^{3}-16a^{2}-43a-4$ |
| 64.1-a1 |
64.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$178.50016$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.015642054$ |
$60397.25256$ |
4.01308 |
\( 3595 a^{5} - 12330 a^{4} - \frac{8429}{2} a^{3} + 27569 a^{2} + \frac{10687}{2} a - \frac{4527}{2} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 15 a^{2} + 7 a - 1\) , \( -a^{4} + 4 a^{3} + a^{2} - 11 a\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 2\) , \( 3 a^{5} - 11 a^{4} - a^{3} + 27 a^{2} - 8 a - 1\) , \( a^{5} - 4 a^{4} + 2 a^{3} + 9 a^{2} - 10 a - 2\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+15a^{2}+7a-1\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+8a+2\right){y}={x}^{3}+\left(-a^{4}+4a^{3}+a^{2}-11a\right){x}^{2}+\left(3a^{5}-11a^{4}-a^{3}+27a^{2}-8a-1\right){x}+a^{5}-4a^{4}+2a^{3}+9a^{2}-10a-2$ |
| 64.1-b1 |
64.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{6} \) |
$178.50016$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.080428608$ |
$14742.01890$ |
5.03656 |
\( 81626266 a^{5} - \frac{533240161}{2} a^{4} - 152122529 a^{3} + 682397210 a^{2} + 115359997 a - \frac{128915831}{2} \) |
\( \bigl[1\) , \( 3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 17 a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + 5 a\) , \( -3 a^{5} + 7 a^{4} + 16 a^{3} - 24 a^{2} - 28 a + 8\) , \( a^{5} - a^{4} - 10 a^{3} + 8 a^{2} + 18 a - 5\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+5a\right){y}={x}^{3}+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+17a-4\right){x}^{2}+\left(-3a^{5}+7a^{4}+16a^{3}-24a^{2}-28a+8\right){x}+a^{5}-a^{4}-10a^{3}+8a^{2}+18a-5$ |
| 64.1-c1 |
64.1-c |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$178.50016$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.069176298$ |
$3525.281002$ |
2.07180 |
\( 28852252 a^{5} - 49516164 a^{4} - \frac{368017403}{2} a^{3} + 124275717 a^{2} + \frac{1483224203}{4} a + \frac{235794097}{2} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 6 a - 4\) , \( -a^{5} + 4 a^{4} - a^{3} - 10 a^{2} + 8 a + 5\) , \( a + 1\) , \( 48 a^{5} - 120 a^{4} - 224 a^{3} + 387 a^{2} + 383 a - 109\) , \( 285 a^{5} - 670 a^{4} - 1485 a^{3} + 2276 a^{2} + 2620 a - 741\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+6a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-a^{3}-10a^{2}+8a+5\right){x}^{2}+\left(48a^{5}-120a^{4}-224a^{3}+387a^{2}+383a-109\right){x}+285a^{5}-670a^{4}-1485a^{3}+2276a^{2}+2620a-741$ |
| 64.1-d1 |
64.1-d |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{6} \) |
$178.50016$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.149506014$ |
$8225.560611$ |
5.22385 |
\( \frac{44705}{2} a^{5} - \frac{92119}{2} a^{4} - 113966 a^{3} + \frac{270417}{2} a^{2} + 159483 a - 55085 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 8 a^{3} + 14 a^{2} + 13 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 3\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 10 a - 4\) , \( -3 a^{5} + 13 a^{4} - 2 a^{3} - 28 a^{2} + 7 a + 2\) , \( -52 a^{5} + 179 a^{4} + 65 a^{3} - 413 a^{2} - 62 a + 37\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-8a^{3}+14a^{2}+13a-2\right){x}{y}+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+10a-4\right){y}={x}^{3}+\left(a^{5}-4a^{4}+10a^{2}-2a-3\right){x}^{2}+\left(-3a^{5}+13a^{4}-2a^{3}-28a^{2}+7a+2\right){x}-52a^{5}+179a^{4}+65a^{3}-413a^{2}-62a+37$ |
| 64.1-e1 |
64.1-e |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$178.50016$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.007639594$ |
$68527.16618$ |
4.44764 |
\( \frac{1067409}{2} a^{5} - \frac{7240275}{4} a^{4} - \frac{2359609}{4} a^{3} + \frac{7928695}{2} a^{2} + \frac{1257479}{2} a - 365209 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a\) , \( a^{4} - 4 a^{3} + 10 a - 2\) , \( 2 a^{5} - 5 a^{4} - 9 a^{3} + 15 a^{2} + 16 a - 3\) , \( 8 a^{5} - 26 a^{4} - 18 a^{3} + 69 a^{2} + 29 a - 12\) , \( -60 a^{5} + 150 a^{4} + 277 a^{3} - 474 a^{2} - 475 a + 137\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a\right){x}{y}+\left(2a^{5}-5a^{4}-9a^{3}+15a^{2}+16a-3\right){y}={x}^{3}+\left(a^{4}-4a^{3}+10a-2\right){x}^{2}+\left(8a^{5}-26a^{4}-18a^{3}+69a^{2}+29a-12\right){x}-60a^{5}+150a^{4}+277a^{3}-474a^{2}-475a+137$ |
| 79.1-a1 |
79.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79 \) |
$181.65995$ |
$(a^4-4a^2-2a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1429.758381$ |
1.01223 |
\( -\frac{44836108275}{79} a^{5} + \frac{78851929406}{79} a^{4} + \frac{288073579176}{79} a^{3} - \frac{199584057672}{79} a^{2} - \frac{586249976912}{79} a - \frac{186119580259}{79} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 15 a^{2} + 6 a - 2\) , \( a^{5} - 4 a^{4} - a^{3} + 12 a^{2} + 2 a - 3\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 14 a^{2} + 12 a - 2\) , \( a^{5} - 6 a^{4} + a^{3} + 22 a^{2} + 4 a - 7\) , \( -3 a^{4} + 2 a^{3} + 16 a^{2} + 6 a - 5\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+15a^{2}+6a-2\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+14a^{2}+12a-2\right){y}={x}^{3}+\left(a^{5}-4a^{4}-a^{3}+12a^{2}+2a-3\right){x}^{2}+\left(a^{5}-6a^{4}+a^{3}+22a^{2}+4a-7\right){x}-3a^{4}+2a^{3}+16a^{2}+6a-5$ |
| 89.1-a1 |
89.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
89.1 |
\( 89 \) |
\( - 89^{5} \) |
$183.47326$ |
$(a^5-4a^4+9a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.136951433$ |
$1976.292961$ |
5.74850 |
\( -\frac{610416408676924}{5584059449} a^{5} + \frac{310176844536316}{5584059449} a^{4} + \frac{3444414648718630}{5584059449} a^{3} + \frac{2047727255962673}{5584059449} a^{2} - \frac{1014620188813505}{5584059449} a - \frac{521605980681600}{5584059449} \) |
\( \bigl[a + 1\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} - 6 a + 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 3\) , \( -28 a^{5} + 68 a^{4} + 139 a^{3} - 225 a^{2} - 245 a + 67\) , \( -157 a^{5} + 377 a^{4} + 791 a^{3} - 1258 a^{2} - 1383 a + 391\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-8a^{2}-6a+1\right){x}^{2}+\left(-28a^{5}+68a^{4}+139a^{3}-225a^{2}-245a+67\right){x}-157a^{5}+377a^{4}+791a^{3}-1258a^{2}-1383a+391$ |
| 89.1-b1 |
89.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
89.1 |
\( 89 \) |
\( -89 \) |
$183.47326$ |
$(a^5-4a^4+9a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.020812526$ |
$57621.46051$ |
5.09419 |
\( -\frac{6429818}{89} a^{5} + \frac{7151722}{89} a^{4} + \frac{38273377}{89} a^{3} - \frac{2190247}{89} a^{2} - \frac{44139643}{89} a - \frac{15296631}{89} \) |
\( \bigl[a + 1\) , \( -3 a^{5} + 9 a^{4} + 8 a^{3} - 24 a^{2} - 11 a + 4\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 5 a - 4\) , \( 2 a^{5} - 8 a^{4} + 2 a^{3} + 15 a^{2} - 8 a + 2\) , \( 5 a^{5} - 18 a^{4} - 3 a^{3} + 38 a^{2} + 4 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+5a-4\right){y}={x}^{3}+\left(-3a^{5}+9a^{4}+8a^{3}-24a^{2}-11a+4\right){x}^{2}+\left(2a^{5}-8a^{4}+2a^{3}+15a^{2}-8a+2\right){x}+5a^{5}-18a^{4}-3a^{3}+38a^{2}+4a-4$ |
| 89.1-c1 |
89.1-c |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
89.1 |
\( 89 \) |
\( - 89^{5} \) |
$183.47326$ |
$(a^5-4a^4+9a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2453.884187$ |
1.73728 |
\( -\frac{31173027562694258152}{5584059449} a^{5} - \frac{25943262191404081928}{5584059449} a^{4} + \frac{113560995120857012869}{5584059449} a^{3} + \frac{134592894286112992859}{5584059449} a^{2} + \frac{7120634447919116776}{5584059449} a - \frac{11006626157853205029}{5584059449} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 6 a^{2} - 2 a - 2\) , \( 3 a^{5} - 9 a^{4} - 8 a^{3} + 24 a^{2} + 11 a - 5\) , \( 8 a^{5} - 26 a^{4} - 17 a^{3} + 66 a^{2} + 19 a - 2\) , \( 22 a^{5} - 62 a^{4} - 83 a^{3} + 162 a^{2} + 146 a + 23\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a\right){x}{y}+\left(3a^{5}-9a^{4}-8a^{3}+24a^{2}+11a-5\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-6a^{2}-2a-2\right){x}^{2}+\left(8a^{5}-26a^{4}-17a^{3}+66a^{2}+19a-2\right){x}+22a^{5}-62a^{4}-83a^{3}+162a^{2}+146a+23$ |
| 101.1-a1 |
101.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
101.1 |
\( 101 \) |
\( - 101^{5} \) |
$185.41736$ |
$(a^5-4a^4+a^3+8a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2981.933428$ |
2.11112 |
\( -\frac{71885353566647}{10510100501} a^{5} + \frac{97666624704233}{10510100501} a^{4} + \frac{549853296058458}{10510100501} a^{3} - \frac{225104783872211}{10510100501} a^{2} - \frac{1197904056116878}{10510100501} a - \frac{482411706450094}{10510100501} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 6 a^{2} + 13 a\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 12 a - 1\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 16 a^{2} + 5 a - 3\) , \( 4 a^{5} - 18 a^{4} - 14 a^{3} + 52 a^{2} + 33 a\) , \( 25 a^{5} + 24 a^{4} - 96 a^{3} - 117 a^{2} + 3 a + 12\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+6a^{2}+13a\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+16a^{2}+5a-3\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+12a-1\right){x}^{2}+\left(4a^{5}-18a^{4}-14a^{3}+52a^{2}+33a\right){x}+25a^{5}+24a^{4}-96a^{3}-117a^{2}+3a+12$ |
| 101.1-b1 |
101.1-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
101.1 |
\( 101 \) |
\( 101^{4} \) |
$185.41736$ |
$(a^5-4a^4+a^3+8a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.009507793$ |
$29459.34042$ |
4.75914 |
\( \frac{745656665841}{104060401} a^{5} - \frac{2351763419617}{104060401} a^{4} - \frac{1425383030276}{104060401} a^{3} + \frac{5220155710262}{104060401} a^{2} + \frac{2147809758780}{104060401} a + \frac{68208384483}{104060401} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 13 a - 1\) , \( 3 a^{5} - 9 a^{4} - 8 a^{3} + 24 a^{2} + 11 a - 6\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 10 a - 4\) , \( -5 a^{4} + 2 a^{3} + 19 a^{2} + 3 a - 8\) , \( 4 a^{5} - 9 a^{4} - 17 a^{3} + 24 a^{2} + 28 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+13a-1\right){x}{y}+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+10a-4\right){y}={x}^{3}+\left(3a^{5}-9a^{4}-8a^{3}+24a^{2}+11a-6\right){x}^{2}+\left(-5a^{4}+2a^{3}+19a^{2}+3a-8\right){x}+4a^{5}-9a^{4}-17a^{3}+24a^{2}+28a-1$ |
| 101.1-c1 |
101.1-c |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
101.1 |
\( 101 \) |
\( 101^{2} \) |
$185.41736$ |
$(a^5-4a^4+a^3+8a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.007405208$ |
$83710.21395$ |
5.26638 |
\( \frac{316727250}{10201} a^{5} - \frac{181537658}{10201} a^{4} - \frac{3004910771}{10201} a^{3} + \frac{292873631}{10201} a^{2} + \frac{6263967194}{10201} a + \frac{2207274147}{10201} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a\) , \( a^{5} - 4 a^{4} - a^{3} + 12 a^{2} - 4\) , \( 3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 18 a - 4\) , \( a^{5} - 6 a^{4} + 6 a^{3} + 14 a^{2} - 18 a - 8\) , \( 9 a^{5} - 21 a^{4} - 44 a^{3} + 57 a^{2} + 83 a + 11\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+2a\right){x}{y}+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+18a-4\right){y}={x}^{3}+\left(a^{5}-4a^{4}-a^{3}+12a^{2}-4\right){x}^{2}+\left(a^{5}-6a^{4}+6a^{3}+14a^{2}-18a-8\right){x}+9a^{5}-21a^{4}-44a^{3}+57a^{2}+83a+11$ |
| 109.1-a1 |
109.1-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
109.1 |
\( 109 \) |
\( 109^{2} \) |
$186.59893$ |
$(2a^5-7a^4-2a^3+16a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.451858234$ |
$1295.225731$ |
4.97215 |
\( \frac{1637084701543}{11881} a^{5} - \frac{5612177278084}{11881} a^{4} - \frac{1789909761683}{11881} a^{3} + \frac{12331930337592}{11881} a^{2} + \frac{1997402084304}{11881} a - \frac{1117323849143}{11881} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 9 a\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( 2 a^{5} - 5 a^{4} - 9 a^{3} + 15 a^{2} + 16 a - 2\) , \( 2 a^{5} - 5 a^{4} - 12 a^{3} + 15 a^{2} + 18 a - 5\) , \( 2 a^{5} - 4 a^{4} - 16 a^{3} + 10 a - 3\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+9a\right){x}{y}+\left(2a^{5}-5a^{4}-9a^{3}+15a^{2}+16a-2\right){y}={x}^3+\left(-a^{3}+a^{2}+3a+1\right){x}^2+\left(2a^{5}-5a^{4}-12a^{3}+15a^{2}+18a-5\right){x}+2a^{5}-4a^{4}-16a^{3}+10a-3$ |
| 121.3-a1 |
121.3-a |
$2$ |
$2$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.3 |
\( 11^{2} \) |
\( 11^{10} \) |
$188.23009$ |
$(a-1), (-a^2+2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6895.576085$ |
1.22047 |
\( \frac{9849575381}{161051} a^{5} - \frac{30832388967}{161051} a^{4} - \frac{1990343167}{14641} a^{3} + \frac{79130927245}{161051} a^{2} + \frac{22098713421}{161051} a - \frac{4178677423}{161051} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 14 a - 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a + 1\) , \( 8 a^{5} - 32 a^{4} + 7 a^{3} + 56 a^{2} - 5 a - 7\) , \( 110 a^{5} - 375 a^{4} - 134 a^{3} + 852 a^{2} + 129 a - 80\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+14a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-2\right){x}^{2}+\left(8a^{5}-32a^{4}+7a^{3}+56a^{2}-5a-7\right){x}+110a^{5}-375a^{4}-134a^{3}+852a^{2}+129a-80$ |
| 121.3-a2 |
121.3-a |
$2$ |
$2$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.3 |
\( 11^{2} \) |
\( - 11^{20} \) |
$188.23009$ |
$(a-1), (-a^2+2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$430.9735053$ |
1.22047 |
\( -\frac{356344659261087119}{25937424601} a^{5} + \frac{1223576702770650997}{25937424601} a^{4} + \frac{383786298109420955}{25937424601} a^{3} - \frac{2688153987666502166}{25937424601} a^{2} - \frac{422074671524804754}{25937424601} a + \frac{248579777643501658}{25937424601} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 14 a - 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a + 1\) , \( 323 a^{5} - 1112 a^{4} - 338 a^{3} + 2436 a^{2} + 370 a - 227\) , \( 5081 a^{5} - 17440 a^{4} - 5509 a^{3} + 38377 a^{2} + 6021 a - 3550\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+14a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-2\right){x}^{2}+\left(323a^{5}-1112a^{4}-338a^{3}+2436a^{2}+370a-227\right){x}+5081a^{5}-17440a^{4}-5509a^{3}+38377a^{2}+6021a-3550$ |
| 121.5-a1 |
121.5-a |
$2$ |
$3$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.5 |
\( 11^{2} \) |
\( 11^{6} \) |
$188.23009$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.662683093$ |
$2000.775042$ |
5.63210 |
\( -713527881 a^{5} + 2330801731 a^{4} + 1329458751 a^{3} - 5965582626 a^{2} - 1007746483 a + 563755026 \) |
\( \bigl[a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 18 a - 4\) , \( 7 a^{5} - 17 a^{4} - 32 a^{3} + 54 a^{2} + 54 a - 17\) , \( 19 a^{5} - 46 a^{4} - 92 a^{3} + 150 a^{2} + 159 a - 46\bigr] \) |
${y}^2+a{x}{y}+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+18a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}^{2}+\left(7a^{5}-17a^{4}-32a^{3}+54a^{2}+54a-17\right){x}+19a^{5}-46a^{4}-92a^{3}+150a^{2}+159a-46$ |
| 121.5-a2 |
121.5-a |
$2$ |
$3$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.5 |
\( 11^{2} \) |
\( 11^{6} \) |
$188.23009$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1.988049281$ |
$74.10277933$ |
5.63210 |
\( -3173411505733159920311156467 a^{5} + 10365486659128555248808418347 a^{4} + 5914089315880839869937229951 a^{3} - 26529802106967835674458663364 a^{2} - 4484806235806003425212549021 a + 2505942638562922589671094273 \) |
\( \bigl[a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 3 a^{5} - 8 a^{4} - 11 a^{3} + 22 a^{2} + 18 a - 4\) , \( -68 a^{5} + 188 a^{4} + 268 a^{3} - 576 a^{2} - 451 a + 123\) , \( -208 a^{5} + 533 a^{4} + 858 a^{3} - 1563 a^{2} - 1301 a + 350\bigr] \) |
${y}^2+a{x}{y}+\left(3a^{5}-8a^{4}-11a^{3}+22a^{2}+18a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}^{2}+\left(-68a^{5}+188a^{4}+268a^{3}-576a^{2}-451a+123\right){x}-208a^{5}+533a^{4}+858a^{3}-1563a^{2}-1301a+350$ |
| 121.5-b1 |
121.5-b |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.5 |
\( 11^{2} \) |
\( - 11^{3} \) |
$188.23009$ |
$(a^2-a-1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.026679591$ |
$6828.956547$ |
9.28712 |
\( -1656 a^{5} + 1166 a^{4} + 10452 a^{3} + 2562 a^{2} - 10239 a - 3522 \) |
\( \bigl[3 a^{5} - 9 a^{4} - 8 a^{3} + 24 a^{2} + 10 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 5 a^{2} - 9 a\) , \( 2 a^{5} - 5 a^{4} - 8 a^{3} + 13 a^{2} + 14 a\) , \( -2 a^{5} - 2 a^{4} + 35 a^{3} - 12 a^{2} - 78 a + 13\) , \( 21 a^{5} - 57 a^{4} - 81 a^{3} + 171 a^{2} + 123 a - 47\bigr] \) |
${y}^2+\left(3a^{5}-9a^{4}-8a^{3}+24a^{2}+10a-4\right){x}{y}+\left(2a^{5}-5a^{4}-8a^{3}+13a^{2}+14a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-5a^{2}-9a\right){x}^{2}+\left(-2a^{5}-2a^{4}+35a^{3}-12a^{2}-78a+13\right){x}+21a^{5}-57a^{4}-81a^{3}+171a^{2}+123a-47$ |
| 121.5-c1 |
121.5-c |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.5 |
\( 11^{2} \) |
\( - 11^{9} \) |
$188.23009$ |
$(a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1954.221776$ |
2.76706 |
\( -1656 a^{5} + 1166 a^{4} + 10452 a^{3} + 2562 a^{2} - 10239 a - 3522 \) |
\( \bigl[a^{4} - 3 a^{3} - 2 a^{2} + 7 a + 2\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 6 a^{2} - 7 a + 1\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 15 a^{2} + 6 a - 1\) , \( 4 a^{5} - 15 a^{4} + 35 a^{2} - 12 a\) , \( -19 a^{5} + 57 a^{4} + 53 a^{3} - 156 a^{2} - 67 a + 24\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-2a^{2}+7a+2\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+15a^{2}+6a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-6a^{2}-7a+1\right){x}^{2}+\left(4a^{5}-15a^{4}+35a^{2}-12a\right){x}-19a^{5}+57a^{4}+53a^{3}-156a^{2}-67a+24$ |
| 121.5-d1 |
121.5-d |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.5 |
\( 11^{2} \) |
\( 11^{6} \) |
$188.23009$ |
$(a^2-a-1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5Nn.3.2[2] |
|
\( 1 \) |
$1$ |
$379.4556315$ |
5.68738 |
\( 69618230 a^{5} + 90964008 a^{4} - 1295258299 a^{3} + 451586144 a^{2} + 2806547659 a - 684726662 \) |
\( \bigl[2 a^{5} - 6 a^{4} - 6 a^{3} + 17 a^{2} + 10 a - 3\) , \( a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + 6 a - 1\) , \( -23 a^{5} + 75 a^{4} + 44 a^{3} - 194 a^{2} - 34 a + 16\) , \( -71 a^{5} + 233 a^{4} + 131 a^{3} - 601 a^{2} - 102 a + 56\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-6a^{3}+17a^{2}+10a-3\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+6a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-23a^{5}+75a^{4}+44a^{3}-194a^{2}-34a+16\right){x}-71a^{5}+233a^{4}+131a^{3}-601a^{2}-102a+56$ |
| 121.6-a1 |
121.6-a |
$1$ |
$1$ |
6.6.1995125.1 |
$6$ |
$[6, 0]$ |
121.6 |
\( 11^{2} \) |
\( - 11^{10} \) |
$188.23009$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.274053498$ |
$1099.626788$ |
5.95113 |
\( -196922 a^{5} + 644596 a^{4} + 361115 a^{3} - 1641968 a^{2} - 274151 a + 155060 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 9 a^{3} + 15 a^{2} + 16 a - 3\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 18 a^{2} - 2 a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 3\) , \( a^{5} - 5 a^{4} + 12 a^{3} + a^{2} - 33 a + 12\) , \( -3 a^{5} + 10 a^{4} + 22 a^{3} - 59 a^{2} - 74 a + 19\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-9a^{3}+15a^{2}+16a-3\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-3\right){y}={x}^{3}+\left(2a^{5}-7a^{4}-2a^{3}+18a^{2}-2a-4\right){x}^{2}+\left(a^{5}-5a^{4}+12a^{3}+a^{2}-33a+12\right){x}-3a^{5}+10a^{4}+22a^{3}-59a^{2}-74a+19$ |
*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.
