| 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 |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$66.41215114$ |
1.08106 |
\( 19474670538763427899835134 a^{5} - 36080571172172091729315071 a^{4} - 86082399830164896682940146 a^{3} + 151300477323797471293148922 a^{2} + 26784619923736808673257449 a - 22839037819505453842362392 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 9 a - 3\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 13 a^{2} - a + 4\) , \( a^{4} - 4 a^{2}\) , \( -48 a^{5} + 52 a^{4} + 263 a^{3} - 187 a^{2} - 274 a - 80\) , \( 84 a^{5} - 5 a^{4} - 609 a^{3} - 85 a^{2} + 1086 a + 364\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+9a-3\right){x}{y}+\left(a^{4}-4a^{2}\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+4a^{3}-13a^{2}-a+4\right){x}^{2}+\left(-48a^{5}+52a^{4}+263a^{3}-187a^{2}-274a-80\right){x}+84a^{5}-5a^{4}-609a^{3}-85a^{2}+1086a+364$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$4250.377673$ |
1.08106 |
\( 2054572933123 a^{5} - 3806472830974 a^{4} - 9081684033552 a^{3} + 15962080935930 a^{2} + 2825825943557 a - 2409472851201 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 5 a - 3\) , \( -2 a^{5} + 4 a^{4} + 11 a^{3} - 17 a^{2} - 11 a + 4\) , \( a^{3} - 4 a + 1\) , \( 13 a^{5} + 15 a^{4} - 57 a^{3} - 73 a^{2} - a + 11\) , \( -35 a^{5} - 78 a^{4} + 136 a^{3} + 373 a^{2} + 99 a - 81\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+5a-3\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+11a^{3}-17a^{2}-11a+4\right){x}^{2}+\left(13a^{5}+15a^{4}-57a^{3}-73a^{2}-a+11\right){x}-35a^{5}-78a^{4}+136a^{3}+373a^{2}+99a-81$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$17001.51069$ |
1.08106 |
\( -667583 a^{5} + 1237075 a^{4} + 2952749 a^{3} - 5185620 a^{2} - 925493 a + 778938 \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 4 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} - a - 1\) , \( 0\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} + a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-4a+1\right){x}{y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}-a-1\right){x}^{2}+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}+a-1\right){x}$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$1062.594418$ |
1.08106 |
\( 556779921550594 a^{5} - 106754774129409 a^{4} - 3082371640850702 a^{3} + 242553391812870 a^{2} + 3585132400605207 a + 1277071891174888 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 5 a - 3\) , \( -2 a^{5} + 4 a^{4} + 11 a^{3} - 17 a^{2} - 11 a + 4\) , \( a^{3} - 4 a + 1\) , \( 223 a^{5} + 185 a^{4} - 997 a^{3} - 943 a^{2} + 64 a + 121\) , \( -4123 a^{5} - 3500 a^{4} + 18390 a^{3} + 17523 a^{2} - 1117 a - 2304\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+5a-3\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+11a^{3}-17a^{2}-11a+4\right){x}^{2}+\left(223a^{5}+185a^{4}-997a^{3}-943a^{2}+64a+121\right){x}-4123a^{5}-3500a^{4}+18390a^{3}+17523a^{2}-1117a-2304$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$256$ |
\( 1 \) |
$1$ |
$16.60303778$ |
1.08106 |
\( 356459972164537495327700357008 a^{5} + 402987734353157748130004694449 a^{4} - 1280183458336239721487620938927 a^{3} - 1301625934367094844928288950083 a^{2} + 78530173459325852078887625003 a + 167310679412254516890791962246 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} + a - 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 5 a^{2} - 3 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a + 1\) , \( -733 a^{5} + 1064 a^{4} + 3976 a^{3} - 4687 a^{2} - 4007 a + 1557\) , \( 6118 a^{5} - 8921 a^{4} - 33071 a^{3} + 39284 a^{2} + 32890 a - 13568\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}+a-3\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-5a^{2}-3a+4\right){x}^{2}+\left(-733a^{5}+1064a^{4}+3976a^{3}-4687a^{2}-4007a+1557\right){x}+6118a^{5}-8921a^{4}-33071a^{3}+39284a^{2}+32890a-13568$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$265.6486045$ |
1.08106 |
\( 988785583160956036924620939376 a^{5} - 652401789820580037039302100401 a^{4} - 6154659887120339786787677655889 a^{3} + 1861333649743152428946807060291 a^{2} + 8543508373678681050396362612437 a + 2906492372174480271546458107722 \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 4 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} - a - 1\) , \( 0\) , \( 456 a^{5} + 438 a^{4} - 1989 a^{3} - 2196 a^{2} - 219 a + 124\) , \( -15782 a^{5} - 13652 a^{4} + 69706 a^{3} + 67620 a^{2} - 2124 a - 7753\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-4a+1\right){x}{y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}-a-1\right){x}^{2}+\left(456a^{5}+438a^{4}-1989a^{3}-2196a^{2}-219a+124\right){x}-15782a^{5}-13652a^{4}+69706a^{3}+67620a^{2}-2124a-7753$ |
| 1.1-b1 |
1.1-b |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$2645.941172$ |
0.672982 |
\( 19474670538763427899835134 a^{5} - 36080571172172091729315071 a^{4} - 86082399830164896682940146 a^{3} + 151300477323797471293148922 a^{2} + 26784619923736808673257449 a - 22839037819505453842362392 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( 9 a^{5} - 5 a^{4} - 65 a^{3} + 29 a^{2} + 111 a - 43\) , \( -47 a^{5} + 48 a^{4} + 277 a^{3} - 226 a^{2} - 339 a + 129\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+5a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(9a^{5}-5a^{4}-65a^{3}+29a^{2}+111a-43\right){x}-47a^{5}+48a^{4}+277a^{3}-226a^{2}-339a+129$ |
| 1.1-b2 |
1.1-b |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$10583.76468$ |
0.672982 |
\( 2054572933123 a^{5} - 3806472830974 a^{4} - 9081684033552 a^{3} + 15962080935930 a^{2} + 2825825943557 a - 2409472851201 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( -a^{5} + 5 a^{3} - a^{2} - 4 a - 3\) , \( -a^{5} - a^{4} + 5 a^{3} + 2 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+5a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(-a^{5}+5a^{3}-a^{2}-4a-3\right){x}-a^{5}-a^{4}+5a^{3}+2a^{2}-3a-1$ |
| 1.1-b3 |
1.1-b |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$42335.05875$ |
0.672982 |
\( -667583 a^{5} + 1237075 a^{4} + 2952749 a^{3} - 5185620 a^{2} - 925493 a + 778938 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( -a^{5} + 5 a^{3} - a^{2} - 4 a + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} - 1\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+5a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(-a^{5}+5a^{3}-a^{2}-4a+2\right){x}+a^{5}-2a^{4}-4a^{3}+8a^{2}-1$ |
| 1.1-b4 |
1.1-b |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$64$ |
\( 1 \) |
$1$ |
$165.3713232$ |
0.672982 |
\( 556779921550594 a^{5} - 106754774129409 a^{4} - 3082371640850702 a^{3} + 242553391812870 a^{2} + 3585132400605207 a + 1277071891174888 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( -11 a^{5} + 5 a^{4} + 75 a^{3} - 31 a^{2} - 119 a - 43\) , \( -43 a^{5} - 6 a^{4} + 269 a^{3} - 34 a^{2} - 359 a - 131\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+5a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(-11a^{5}+5a^{4}+75a^{3}-31a^{2}-119a-43\right){x}-43a^{5}-6a^{4}+269a^{3}-34a^{2}-359a-131$ |
| 1.1-b5 |
1.1-b |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1024$ |
\( 1 \) |
$1$ |
$2.583926926$ |
0.672982 |
\( 356459972164537495327700357008 a^{5} + 402987734353157748130004694449 a^{4} - 1280183458336239721487620938927 a^{3} - 1301625934367094844928288950083 a^{2} + 78530173459325852078887625003 a + 167310679412254516890791962246 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 5 a - 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 9 a^{2} + 3\) , \( a^{5} - 4 a^{3} + a + 1\) , \( -1286 a^{5} + 999 a^{4} + 7837 a^{3} - 3306 a^{2} - 10422 a - 2742\) , \( -35408 a^{5} + 24252 a^{4} + 219325 a^{3} - 71953 a^{2} - 301614 a - 97652\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+5a-3\right){x}{y}+\left(a^{5}-4a^{3}+a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-9a^{2}+3\right){x}^{2}+\left(-1286a^{5}+999a^{4}+7837a^{3}-3306a^{2}-10422a-2742\right){x}-35408a^{5}+24252a^{4}+219325a^{3}-71953a^{2}-301614a-97652$ |
| 1.1-b6 |
1.1-b |
$6$ |
$8$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$87.83249$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1024$ |
\( 1 \) |
$1$ |
$2.583926926$ |
0.672982 |
\( 988785583160956036924620939376 a^{5} - 652401789820580037039302100401 a^{4} - 6154659887120339786787677655889 a^{3} + 1861333649743152428946807060291 a^{2} + 8543508373678681050396362612437 a + 2906492372174480271546458107722 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( -106 a^{5} + 220 a^{4} + 870 a^{3} - 811 a^{2} - 1899 a - 658\) , \( -1633 a^{5} + 3188 a^{4} + 12789 a^{3} - 11679 a^{2} - 26523 a - 8620\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+5a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(-106a^{5}+220a^{4}+870a^{3}-811a^{2}-1899a-658\right){x}-1633a^{5}+3188a^{4}+12789a^{3}-11679a^{2}-26523a-8620$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$107.26004$ |
$(a^3-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4005.949440$ |
2.03779 |
\( \frac{26409275481}{14641} a^{5} - \frac{37964648544}{14641} a^{4} - \frac{141838839729}{14641} a^{3} + \frac{167713909763}{14641} a^{2} + \frac{137868294632}{14641} a - \frac{60345357700}{14641} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} - 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - a + 3\) , \( 0\) , \( -a^{2} + a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+5a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}-a+3\right){x}^{2}+\left(-a^{2}+a+2\right){x}$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$107.26004$ |
$(a^3-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1001.487360$ |
2.03779 |
\( -\frac{2073398676004049181537}{214358881} a^{5} + \frac{2980851192898443467617}{214358881} a^{4} + \frac{11135780014883593519015}{214358881} a^{3} - \frac{13167327751171658528183}{214358881} a^{2} - \frac{10824320631915953239657}{214358881} a + \frac{4737418469535071469153}{214358881} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} - 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - a + 3\) , \( 0\) , \( 4 a^{2} - 4 a - 8\) , \( -a^{5} - a^{4} + 6 a^{3} + 14 a^{2} - 16 a - 22\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+5a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}-a+3\right){x}^{2}+\left(4a^{2}-4a-8\right){x}-a^{5}-a^{4}+6a^{3}+14a^{2}-16a-22$ |
| 11.1-b1 |
11.1-b |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$107.26004$ |
$(a^3-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1501.744202$ |
1.52785 |
\( \frac{104855673}{11} a^{5} + \frac{213667626}{11} a^{4} - \frac{470839075}{11} a^{3} - \frac{1001999556}{11} a^{2} - \frac{19437862}{11} a + \frac{137797178}{11} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 9 a\) , \( a^{3} - 4 a\) , \( 2 a^{5} + a^{4} - 9 a^{3} - 4 a^{2} + 2 a + 3\) , \( 2 a^{5} + a^{4} - 8 a^{3} - 3 a^{2}\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-9a\right){x}^{2}+\left(2a^{5}+a^{4}-9a^{3}-4a^{2}+2a+3\right){x}+2a^{5}+a^{4}-8a^{3}-3a^{2}$ |
| 11.1-c1 |
11.1-c |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$107.26004$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.004399879$ |
$85413.69335$ |
2.29405 |
\( \frac{104855673}{11} a^{5} + \frac{213667626}{11} a^{4} - \frac{470839075}{11} a^{3} - \frac{1001999556}{11} a^{2} - \frac{19437862}{11} a + \frac{137797178}{11} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} + a + 3\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 4 a - 2\) , \( -a^{5} + 5 a^{3} - 5 a\) , \( -4 a^{5} + 6 a^{4} + 19 a^{3} - 25 a^{2} - 11 a + 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-2\right){x}{y}+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}+a+3\right){x}^{2}+\left(-a^{5}+5a^{3}-5a\right){x}-4a^{5}+6a^{4}+19a^{3}-25a^{2}-11a+2$ |
| 11.1-d1 |
11.1-d |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$107.26004$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.004439684$ |
$69591.14624$ |
1.88600 |
\( \frac{26409275481}{14641} a^{5} - \frac{37964648544}{14641} a^{4} - \frac{141838839729}{14641} a^{3} + \frac{167713909763}{14641} a^{2} + \frac{137868294632}{14641} a - \frac{60345357700}{14641} \) |
\( \bigl[a^{4} - 4 a^{2} + a\) , \( -a^{5} + a^{4} + 4 a^{3} - 4 a^{2} - 1\) , \( 0\) , \( -a^{4} + 4 a^{2}\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-4a^{2}-1\right){x}^{2}+\left(-a^{4}+4a^{2}\right){x}$ |
| 11.1-d2 |
11.1-d |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$107.26004$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.008879369$ |
$17397.78656$ |
1.88600 |
\( -\frac{2073398676004049181537}{214358881} a^{5} + \frac{2980851192898443467617}{214358881} a^{4} + \frac{11135780014883593519015}{214358881} a^{3} - \frac{13167327751171658528183}{214358881} a^{2} - \frac{10824320631915953239657}{214358881} a + \frac{4737418469535071469153}{214358881} \) |
\( \bigl[a^{4} - 4 a^{2} + a\) , \( -a^{5} + a^{4} + 4 a^{3} - 4 a^{2} - 1\) , \( 0\) , \( 4 a^{4} - 16 a^{2}\) , \( 6 a^{5} - 7 a^{4} - 25 a^{3} + 29 a^{2} + 3 a - 1\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-4a^{2}-1\right){x}^{2}+\left(4a^{4}-16a^{2}\right){x}+6a^{5}-7a^{4}-25a^{3}+29a^{2}+3a-1$ |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$112.25818$ |
$(-a^5+a^4+5a^3-4a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2118.810144$ |
2.15564 |
\( -\frac{100354785}{19} a^{5} + \frac{180877580}{19} a^{4} + \frac{443785703}{19} a^{3} - \frac{757153954}{19} a^{2} - \frac{136449958}{19} a + \frac{114297617}{19} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 5 a - 3\) , \( a^{2} + a - 3\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 4 a^{5} + 11 a^{4} - 10 a^{3} - 40 a^{2} - 11 a + 9\) , \( 21 a^{5} + 23 a^{4} - 76 a^{3} - 74 a^{2} + 6 a + 9\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+5a-3\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(4a^{5}+11a^{4}-10a^{3}-40a^{2}-11a+9\right){x}+21a^{5}+23a^{4}-76a^{3}-74a^{2}+6a+9$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$112.25818$ |
$(-a^5+a^4+5a^3-4a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.069246074$ |
$2398.083657$ |
3.04099 |
\( -\frac{5879200135857888129}{6859} a^{5} + \frac{8452315909766973035}{6859} a^{4} + \frac{31575924231995613216}{6859} a^{3} - \frac{37336454040216488053}{6859} a^{2} - \frac{30692769579573544291}{6859} a + \frac{13433128268829124361}{6859} \) |
\( \bigl[a^{5} - 4 a^{3} + a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 4\) , \( a^{4} - 4 a^{2}\) , \( 6 a^{5} + 12 a^{4} - 18 a^{3} - 46 a^{2} - 9 a + 9\) , \( 16 a^{5} + 23 a^{4} - 56 a^{3} - 84 a^{2} + 6 a + 11\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a+1\right){x}{y}+\left(a^{4}-4a^{2}\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-4\right){x}^{2}+\left(6a^{5}+12a^{4}-18a^{3}-46a^{2}-9a+9\right){x}+16a^{5}+23a^{4}-56a^{3}-84a^{2}+6a+11$ |
| 19.1-c1 |
19.1-c |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$112.25818$ |
$(-a^5+a^4+5a^3-4a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1342.388599$ |
1.36572 |
\( -\frac{5879200135857888129}{6859} a^{5} + \frac{8452315909766973035}{6859} a^{4} + \frac{31575924231995613216}{6859} a^{3} - \frac{37336454040216488053}{6859} a^{2} - \frac{30692769579573544291}{6859} a + \frac{13433128268829124361}{6859} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 5 a - 3\) , \( a^{3} - a^{2} - 5 a + 2\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 9 a - 3\) , \( -a^{5} + 14 a^{4} + 6 a^{3} - 64 a^{2} - 15 a + 12\) , \( 16 a^{5} - 77 a^{4} - 69 a^{3} + 333 a^{2} + 35 a - 47\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+5a-3\right){x}{y}+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+9a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(-a^{5}+14a^{4}+6a^{3}-64a^{2}-15a+12\right){x}+16a^{5}-77a^{4}-69a^{3}+333a^{2}+35a-47$ |
| 19.1-d1 |
19.1-d |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$112.25818$ |
$(-a^5+a^4+5a^3-4a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.004745726$ |
$70232.31896$ |
2.03458 |
\( -\frac{100354785}{19} a^{5} + \frac{180877580}{19} a^{4} + \frac{443785703}{19} a^{3} - \frac{757153954}{19} a^{2} - \frac{136449958}{19} a + \frac{114297617}{19} \) |
\( \bigl[a^{5} - 5 a^{3} + 5 a + 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} + a - 2\) , \( -2 a^{5} + 4 a^{4} + 11 a^{3} - 18 a^{2} - 11 a + 9\) , \( 4 a^{4} + a^{3} - 16 a^{2} - 2 a + 3\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-2a^{5}+4a^{4}+11a^{3}-18a^{2}-11a+9\right){x}+4a^{4}+a^{3}-16a^{2}-2a+3$ |
| 25.1-a1 |
25.1-a |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$38284.36577$ |
1.55799 |
\( -\frac{4361875424282}{25} a^{5} - \frac{3643603290539}{25} a^{4} + \frac{19490138884948}{25} a^{3} + \frac{18328989803179}{25} a^{2} - \frac{1294139324264}{25} a - \frac{2379725061278}{25} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 3\) , \( 78 a^{5} - 113 a^{4} - 408 a^{3} + 506 a^{2} + 367 a - 203\) , \( 310 a^{5} - 433 a^{4} - 1670 a^{3} + 1905 a^{2} + 1644 a - 648\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-3\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-3a+4\right){x}^{2}+\left(78a^{5}-113a^{4}-408a^{3}+506a^{2}+367a-203\right){x}+310a^{5}-433a^{4}-1670a^{3}+1905a^{2}+1644a-648$ |
| 25.1-a2 |
25.1-a |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{16} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$122.5099704$ |
1.55799 |
\( \frac{40865703}{5} a^{5} - \frac{21511202733}{3125} a^{4} - \frac{186622342323}{3125} a^{3} + \frac{36456605444}{625} a^{2} + \frac{177528999581}{3125} a - \frac{73974132167}{3125} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 8 a - 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 7 a\) , \( a^{5} - 5 a^{3} + 5 a\) , \( 8 a^{5} - 13 a^{4} - 33 a^{3} + 44 a^{2} + 29 a - 15\) , \( 26 a^{5} - 45 a^{4} - 109 a^{3} + 148 a^{2} + 106 a - 50\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+8a-2\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-7a\right){x}^{2}+\left(8a^{5}-13a^{4}-33a^{3}+44a^{2}+29a-15\right){x}+26a^{5}-45a^{4}-109a^{3}+148a^{2}+106a-50$ |
| 25.1-a3 |
25.1-a |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$76568.73154$ |
1.55799 |
\( \frac{932263}{5} a^{5} + \frac{930887}{5} a^{4} - \frac{3904476}{5} a^{3} - \frac{4001671}{5} a^{2} + \frac{219009}{5} a + \frac{523401}{5} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 3\) , \( -17 a^{5} + 27 a^{4} + 97 a^{3} - 119 a^{2} - 108 a + 47\) , \( -3 a^{5} + 9 a^{4} + 21 a^{3} - 38 a^{2} - 31 a + 15\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-3\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-3a+4\right){x}^{2}+\left(-17a^{5}+27a^{4}+97a^{3}-119a^{2}-108a+47\right){x}-3a^{5}+9a^{4}+21a^{3}-38a^{2}-31a+15$ |
| 25.1-a4 |
25.1-a |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{26} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$61.25498523$ |
1.55799 |
\( -\frac{704473882365318296541}{1953125} a^{5} + \frac{5063984613972749673206}{9765625} a^{4} + \frac{18917891393681460753166}{9765625} a^{3} - \frac{4473832517398513998036}{1953125} a^{2} - \frac{18388772312642741920997}{9765625} a + \frac{8048108433855430117114}{9765625} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 8 a - 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 7 a\) , \( a^{5} - 5 a^{3} + 5 a\) , \( 103 a^{5} - 153 a^{4} - 538 a^{3} + 669 a^{2} + 504 a - 265\) , \( 894 a^{5} - 1300 a^{4} - 4763 a^{3} + 5706 a^{2} + 4602 a - 2093\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+8a-2\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-7a\right){x}^{2}+\left(103a^{5}-153a^{4}-538a^{3}+669a^{2}+504a-265\right){x}+894a^{5}-1300a^{4}-4763a^{3}+5706a^{2}+4602a-2093$ |
| 25.1-b1 |
25.1-b |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1374.963908$ |
1.39886 |
\( -\frac{4361875424282}{25} a^{5} - \frac{3643603290539}{25} a^{4} + \frac{19490138884948}{25} a^{3} + \frac{18328989803179}{25} a^{2} - \frac{1294139324264}{25} a - \frac{2379725061278}{25} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a^{5} - 4 a^{3}\) , \( -204 a^{5} + 121 a^{4} + 1290 a^{3} - 299 a^{2} - 1839 a - 713\) , \( -3628 a^{5} + 2407 a^{4} + 22580 a^{3} - 6890 a^{2} - 31334 a - 10623\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{5}-4a^{3}\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+4\right){x}^{2}+\left(-204a^{5}+121a^{4}+1290a^{3}-299a^{2}-1839a-713\right){x}-3628a^{5}+2407a^{4}+22580a^{3}-6890a^{2}-31334a-10623$ |
| 25.1-b2 |
25.1-b |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{16} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2749.927816$ |
1.39886 |
\( \frac{40865703}{5} a^{5} - \frac{21511202733}{3125} a^{4} - \frac{186622342323}{3125} a^{3} + \frac{36456605444}{625} a^{2} + \frac{177528999581}{3125} a - \frac{73974132167}{3125} \) |
\( \bigl[a^{4} - 4 a^{2}\) , \( 2 a^{5} - 4 a^{4} - 9 a^{3} + 17 a^{2} + 3 a - 3\) , \( a^{5} - 4 a^{3} + a + 1\) , \( 10 a^{5} - 25 a^{4} - 49 a^{3} + 103 a^{2} + 30 a - 20\) , \( a^{5} - 19 a^{4} - 3 a^{3} + 72 a^{2} - 12 a - 4\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{5}-4a^{3}+a+1\right){y}={x}^{3}+\left(2a^{5}-4a^{4}-9a^{3}+17a^{2}+3a-3\right){x}^{2}+\left(10a^{5}-25a^{4}-49a^{3}+103a^{2}+30a-20\right){x}+a^{5}-19a^{4}-3a^{3}+72a^{2}-12a-4$ |
| 25.1-b3 |
25.1-b |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2749.927816$ |
1.39886 |
\( \frac{932263}{5} a^{5} + \frac{930887}{5} a^{4} - \frac{3904476}{5} a^{3} - \frac{4001671}{5} a^{2} + \frac{219009}{5} a + \frac{523401}{5} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 2\) , \( -2 a^{5} + 4 a^{4} + 10 a^{3} - 17 a^{2} - 8 a + 4\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a + 1\) , \( -40 a^{5} + 55 a^{4} + 217 a^{3} - 242 a^{2} - 218 a + 84\) , \( -123 a^{5} + 174 a^{4} + 662 a^{3} - 764 a^{2} - 648 a + 257\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+4a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a+1\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+10a^{3}-17a^{2}-8a+4\right){x}^{2}+\left(-40a^{5}+55a^{4}+217a^{3}-242a^{2}-218a+84\right){x}-123a^{5}+174a^{4}+662a^{3}-764a^{2}-648a+257$ |
| 25.1-b4 |
25.1-b |
$4$ |
$10$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{26} \) |
$114.85508$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1374.963908$ |
1.39886 |
\( -\frac{704473882365318296541}{1953125} a^{5} + \frac{5063984613972749673206}{9765625} a^{4} + \frac{18917891393681460753166}{9765625} a^{3} - \frac{4473832517398513998036}{1953125} a^{2} - \frac{18388772312642741920997}{9765625} a + \frac{8048108433855430117114}{9765625} \) |
\( \bigl[a^{4} - 4 a^{2}\) , \( 2 a^{5} - 4 a^{4} - 9 a^{3} + 17 a^{2} + 3 a - 3\) , \( a^{5} - 4 a^{3} + a + 1\) , \( 60 a^{5} - 90 a^{4} - 319 a^{3} + 393 a^{2} + 295 a - 140\) , \( -302 a^{5} + 419 a^{4} + 1611 a^{3} - 1862 a^{2} - 1543 a + 682\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{5}-4a^{3}+a+1\right){y}={x}^{3}+\left(2a^{5}-4a^{4}-9a^{3}+17a^{2}+3a-3\right){x}^{2}+\left(60a^{5}-90a^{4}-319a^{3}+393a^{2}+295a-140\right){x}-302a^{5}+419a^{4}+1611a^{3}-1862a^{2}-1543a+682$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{2} \) |
$114.85508$ |
$(-a^5+2a^4+6a^3-8a^2-8a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2257.002849$ |
2.29623 |
\( \frac{1617544509962}{5} a^{5} - \frac{4876997927878}{5} a^{4} + \frac{122166425336}{5} a^{3} + \frac{6224090990849}{5} a^{2} + \frac{398349359106}{5} a - 160544068141 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 8 a - 3\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 13 a^{2} + a - 4\) , \( 0\) , \( 3 a^{5} - 6 a^{4} - 14 a^{3} + 27 a^{2} + 8 a - 8\) , \( -4 a^{5} + 2 a^{4} + 20 a^{3} - 11 a^{2} - 17 a + 8\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+8a-3\right){x}{y}={x}^{3}+\left(a^{5}-3a^{4}-4a^{3}+13a^{2}+a-4\right){x}^{2}+\left(3a^{5}-6a^{4}-14a^{3}+27a^{2}+8a-8\right){x}-4a^{5}+2a^{4}+20a^{3}-11a^{2}-17a+8$ |
| 25.2-b1 |
25.2-b |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{14} \) |
$114.85508$ |
$(-a^5+2a^4+6a^3-8a^2-8a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.005335557$ |
$14796.78056$ |
3.37349 |
\( \frac{96196657}{625} a^{5} - \frac{27312308}{125} a^{4} - \frac{520111761}{625} a^{3} + \frac{604410283}{625} a^{2} + \frac{516320347}{625} a - \frac{221816736}{625} \) |
\( \bigl[a^{5} - 5 a^{3} + 5 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 7 a - 1\) , \( a^{4} - 4 a^{2} + a\) , \( 15 a^{5} - 16 a^{4} - 78 a^{3} + 73 a^{2} + 73 a - 27\) , \( -21 a^{5} + 41 a^{4} + 120 a^{3} - 175 a^{2} - 129 a + 58\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+5a\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-7a-1\right){x}^{2}+\left(15a^{5}-16a^{4}-78a^{3}+73a^{2}+73a-27\right){x}-21a^{5}+41a^{4}+120a^{3}-175a^{2}-129a+58$ |
| 25.2-c1 |
25.2-c |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{14} \) |
$114.85508$ |
$(-a^5+2a^4+6a^3-8a^2-8a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1023.854739$ |
1.04165 |
\( \frac{96196657}{625} a^{5} - \frac{27312308}{125} a^{4} - \frac{520111761}{625} a^{3} + \frac{604410283}{625} a^{2} + \frac{516320347}{625} a - \frac{221816736}{625} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} + a + 4\) , \( a^{3} - 4 a + 1\) , \( 24 a^{5} - 35 a^{4} - 131 a^{3} + 154 a^{2} + 134 a - 50\) , \( 103 a^{5} - 148 a^{4} - 555 a^{3} + 654 a^{2} + 545 a - 234\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}+a+4\right){x}^{2}+\left(24a^{5}-35a^{4}-131a^{3}+154a^{2}+134a-50\right){x}+103a^{5}-148a^{4}-555a^{3}+654a^{2}+545a-234$ |
| 25.2-d1 |
25.2-d |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{2} \) |
$114.85508$ |
$(-a^5+2a^4+6a^3-8a^2-8a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 1 \) |
$1$ |
$199.1542706$ |
2.33085 |
\( \frac{1617544509962}{5} a^{5} - \frac{4876997927878}{5} a^{4} + \frac{122166425336}{5} a^{3} + \frac{6224090990849}{5} a^{2} + \frac{398349359106}{5} a - 160544068141 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 4 a - 3\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( 6 a^{5} - 12 a^{4} - 33 a^{3} + 54 a^{2} + 38 a - 17\) , \( 28 a^{5} - 46 a^{4} - 152 a^{3} + 202 a^{2} + 153 a - 69\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+4a-3\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+9a-2\right){x}^{2}+\left(6a^{5}-12a^{4}-33a^{3}+54a^{2}+38a-17\right){x}+28a^{5}-46a^{4}-152a^{3}+202a^{2}+153a-69$ |
| 29.1-a1 |
29.1-a |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$116.28447$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.017933975$ |
$57901.96399$ |
3.16938 |
\( \frac{16078608}{841} a^{5} + \frac{20221202}{841} a^{4} - \frac{58122185}{841} a^{3} - \frac{64614950}{841} a^{2} + \frac{2068362}{841} a + \frac{9264928}{841} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a\) , \( -a^{5} + a^{4} + 4 a^{3} - 4 a^{2} - a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 5 a - 2\) , \( -4 a^{5} + 8 a^{4} + 18 a^{3} - 33 a^{2} - 6 a + 5\) , \( 217 a^{5} - 402 a^{4} - 960 a^{3} + 1685 a^{2} + 300 a - 255\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+5a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-4a^{2}-a-1\right){x}^{2}+\left(-4a^{5}+8a^{4}+18a^{3}-33a^{2}-6a+5\right){x}+217a^{5}-402a^{4}-960a^{3}+1685a^{2}+300a-255$ |
| 29.1-a2 |
29.1-a |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$116.28447$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.008966987$ |
$57901.96399$ |
3.16938 |
\( \frac{4659577072236283}{707281} a^{5} + \frac{5284866538730109}{707281} a^{4} - \frac{16749463421765654}{707281} a^{3} - \frac{17045422251528723}{707281} a^{2} + \frac{1026441233007972}{707281} a + \frac{2191020978508668}{707281} \) |
\( \bigl[1\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 4 a - 2\) , \( -48 a^{5} + 100 a^{4} + 217 a^{3} - 427 a^{2} - 83 a + 68\) , \( 360 a^{5} - 685 a^{4} - 1597 a^{3} + 2888 a^{2} + 509 a - 437\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+4a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+9a-3\right){x}^{2}+\left(-48a^{5}+100a^{4}+217a^{3}-427a^{2}-83a+68\right){x}+360a^{5}-685a^{4}-1597a^{3}+2888a^{2}+509a-437$ |
| 29.1-b1 |
29.1-b |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$116.28447$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.051417039$ |
$19722.31501$ |
3.09506 |
\( \frac{16078608}{841} a^{5} + \frac{20221202}{841} a^{4} - \frac{58122185}{841} a^{3} - \frac{64614950}{841} a^{2} + \frac{2068362}{841} a + \frac{9264928}{841} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 9 a - 2\) , \( 8 a^{4} + 3 a^{3} - 31 a^{2} - 4 a + 6\) , \( -9 a^{5} + 39 a^{4} + 46 a^{3} - 156 a^{2} - 23 a + 22\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+5a-2\right){x}{y}+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+9a-2\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(8a^{4}+3a^{3}-31a^{2}-4a+6\right){x}-9a^{5}+39a^{4}+46a^{3}-156a^{2}-23a+22$ |
| 29.1-b2 |
29.1-b |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$116.28447$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.025708519$ |
$19722.31501$ |
3.09506 |
\( \frac{4659577072236283}{707281} a^{5} + \frac{5284866538730109}{707281} a^{4} - \frac{16749463421765654}{707281} a^{3} - \frac{17045422251528723}{707281} a^{2} + \frac{1026441233007972}{707281} a + \frac{2191020978508668}{707281} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 5 a - 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 13 a^{2} - 9 a + 2\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 9 a - 2\) , \( -60 a^{5} + 118 a^{4} + 273 a^{3} - 501 a^{2} - 89 a + 76\) , \( -401 a^{5} + 768 a^{4} + 1765 a^{3} - 3188 a^{2} - 556 a + 480\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+5a-2\right){x}{y}+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+9a-2\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+10a^{3}-13a^{2}-9a+2\right){x}^{2}+\left(-60a^{5}+118a^{4}+273a^{3}-501a^{2}-89a+76\right){x}-401a^{5}+768a^{4}+1765a^{3}-3188a^{2}-556a+480$ |
| 31.2-a1 |
31.2-a |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$116.93253$ |
$(a^2-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2487.229488$ |
2.53046 |
\( \frac{188987486}{31} a^{5} - \frac{272082083}{31} a^{4} - \frac{1014613018}{31} a^{3} + \frac{1202373611}{31} a^{2} + \frac{985030371}{31} a - \frac{434306805}{31} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 4 a - 2\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 8 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 5 a^{2} - 3\) , \( 11 a^{5} - 7 a^{4} - 46 a^{3} + 33 a^{2} + 12 a - 5\) , \( 16 a^{5} - 6 a^{4} - 64 a^{3} + 34 a^{2} + 12 a - 7\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+5a^{2}-3\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+8a-2\right){x}^{2}+\left(11a^{5}-7a^{4}-46a^{3}+33a^{2}+12a-5\right){x}+16a^{5}-6a^{4}-64a^{3}+34a^{2}+12a-7$ |
| 31.2-b1 |
31.2-b |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$116.93253$ |
$(a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.005963385$ |
$59064.27455$ |
2.15007 |
\( \frac{188987486}{31} a^{5} - \frac{272082083}{31} a^{4} - \frac{1014613018}{31} a^{3} + \frac{1202373611}{31} a^{2} + \frac{985030371}{31} a - \frac{434306805}{31} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 11 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 2\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 12 a^{2} - 7 a + 5\) , \( 3 a^{5} - a^{4} - 14 a^{3} + 6 a^{2} + 9 a - 3\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-11a^{3}+9a^{2}+11a-2\right){x}^{2}+\left(-a^{5}+3a^{4}+6a^{3}-12a^{2}-7a+5\right){x}+3a^{5}-a^{4}-14a^{3}+6a^{2}+9a-3$ |
| 59.2-a1 |
59.2-a |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
59.2 |
\( 59 \) |
\( 59^{2} \) |
$123.37473$ |
$(-a^4+a^3+5a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.020076579$ |
$59777.99453$ |
3.66299 |
\( \frac{22268167}{3481} a^{5} - \frac{30003404}{3481} a^{4} - \frac{123184867}{3481} a^{3} + \frac{140436075}{3481} a^{2} + \frac{118349987}{3481} a - \frac{51572183}{3481} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{5} + 3 a^{4} + 5 a^{3} - 13 a^{2} - 5 a + 2\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 4 a - 3\) , \( -3 a^{5} + 14 a^{3} - 5 a + 1\) , \( -a^{5} + 5 a^{4} + 4 a^{3} - 22 a^{2} - 2 a + 3\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+5a^{3}-13a^{2}-5a+2\right){x}^{2}+\left(-3a^{5}+14a^{3}-5a+1\right){x}-a^{5}+5a^{4}+4a^{3}-22a^{2}-2a+3$ |
| 59.2-a2 |
59.2-a |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
59.2 |
\( 59 \) |
\( 59^{4} \) |
$123.37473$ |
$(-a^4+a^3+5a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.010038289$ |
$59777.99453$ |
3.66299 |
\( -\frac{1693236561555539}{12117361} a^{5} + \frac{2494475539745838}{12117361} a^{4} + \frac{8888642596460304}{12117361} a^{3} - \frac{10662202415374603}{12117361} a^{2} - \frac{8651461723628018}{12117361} a + \frac{3804320539994308}{12117361} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 9 a^{2} - 8 a + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} - 3\) , \( -42 a^{5} + 34 a^{4} + 253 a^{3} - 113 a^{2} - 327 a - 90\) , \( 209 a^{5} - 137 a^{4} - 1300 a^{3} + 389 a^{2} + 1801 a + 621\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+8a-3\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}-3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+6a^{3}-9a^{2}-8a+2\right){x}^{2}+\left(-42a^{5}+34a^{4}+253a^{3}-113a^{2}-327a-90\right){x}+209a^{5}-137a^{4}-1300a^{3}+389a^{2}+1801a+621$ |
| 59.2-b1 |
59.2-b |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
59.2 |
\( 59 \) |
\( 59^{2} \) |
$123.37473$ |
$(-a^4+a^3+5a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.129237283$ |
$8972.812194$ |
3.53933 |
\( \frac{22268167}{3481} a^{5} - \frac{30003404}{3481} a^{4} - \frac{123184867}{3481} a^{3} + \frac{140436075}{3481} a^{2} + \frac{118349987}{3481} a - \frac{51572183}{3481} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a\) , \( -2 a^{5} + 4 a^{4} + 10 a^{3} - 17 a^{2} - 7 a + 2\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 9 a^{2} + 9 a - 3\) , \( 4 a^{5} - 10 a^{4} - 19 a^{3} + 42 a^{2} + 10 a - 7\) , \( -5 a^{5} + 5 a^{4} + 20 a^{3} - 21 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a\right){x}{y}+\left(2a^{5}-2a^{4}-10a^{3}+9a^{2}+9a-3\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+10a^{3}-17a^{2}-7a+2\right){x}^{2}+\left(4a^{5}-10a^{4}-19a^{3}+42a^{2}+10a-7\right){x}-5a^{5}+5a^{4}+20a^{3}-21a^{2}+a+1$ |
| 59.2-b2 |
59.2-b |
$2$ |
$2$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
59.2 |
\( 59 \) |
\( 59^{4} \) |
$123.37473$ |
$(-a^4+a^3+5a^2-3a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.064618641$ |
$8972.812194$ |
3.53933 |
\( -\frac{1693236561555539}{12117361} a^{5} + \frac{2494475539745838}{12117361} a^{4} + \frac{8888642596460304}{12117361} a^{3} - \frac{10662202415374603}{12117361} a^{2} - \frac{8651461723628018}{12117361} a + \frac{3804320539994308}{12117361} \) |
\( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 4 a - 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 8 a - 4\) , \( a^{5} - 5 a^{3} + 4 a + 1\) , \( 6 a^{5} - 5 a^{4} - 28 a^{3} + 20 a^{2} + 10 a - 10\) , \( -8 a^{5} + 3 a^{4} + 36 a^{3} - 9 a^{2} - 10 a - 3\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+4a-3\right){x}{y}+\left(a^{5}-5a^{3}+4a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+8a-4\right){x}^{2}+\left(6a^{5}-5a^{4}-28a^{3}+20a^{2}+10a-10\right){x}-8a^{5}+3a^{4}+36a^{3}-9a^{2}-10a-3$ |
| 59.3-a1 |
59.3-a |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59 \) |
$123.37473$ |
$(-2a^5+9a^3-a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.027670102$ |
$22745.96830$ |
3.84193 |
\( -\frac{2426}{59} a^{5} - \frac{13814}{59} a^{4} + \frac{54996}{59} a^{3} + \frac{12868}{59} a^{2} - \frac{78353}{59} a - \frac{32056}{59} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + a - 2\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 8 a\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 4 a - 3\) , \( 2 a^{5} + 6 a^{4} - 7 a^{3} - 22 a^{2} + 3 a + 5\) , \( 8 a^{5} + 13 a^{4} - 31 a^{3} - 50 a^{2} + 3 a + 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+5a^{2}+a-2\right){x}{y}+\left(2a^{5}-3a^{4}-9a^{3}+13a^{2}+4a-3\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+8a\right){x}^{2}+\left(2a^{5}+6a^{4}-7a^{3}-22a^{2}+3a+5\right){x}+8a^{5}+13a^{4}-31a^{3}-50a^{2}+3a+7$ |
| 59.3-b1 |
59.3-b |
$1$ |
$1$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
59.3 |
\( 59 \) |
\( 59 \) |
$123.37473$ |
$(-2a^5+9a^3-a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.011864928$ |
$44854.56145$ |
3.24868 |
\( -\frac{2426}{59} a^{5} - \frac{13814}{59} a^{4} + \frac{54996}{59} a^{3} + \frac{12868}{59} a^{2} - \frac{78353}{59} a - \frac{32056}{59} \) |
\( \bigl[a^{5} - 4 a^{3} + a + 1\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 13 a^{2} - 7 a + 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a\) , \( 6 a^{5} + 13 a^{4} - 17 a^{3} - 45 a^{2} - 10 a + 6\) , \( 23 a^{5} + 30 a^{4} - 80 a^{3} - 99 a^{2} - 2 a + 12\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+6a^{3}-13a^{2}-7a+3\right){x}^{2}+\left(6a^{5}+13a^{4}-17a^{3}-45a^{2}-10a+6\right){x}+23a^{5}+30a^{4}-80a^{3}-99a^{2}-2a+12$ |
| 71.1-a1 |
71.1-a |
$2$ |
$3$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71^{3} \) |
$125.29298$ |
$(2a^5-3a^4-10a^3+12a^2+8a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$34.74976617$ |
2.86365 |
\( \frac{6804367795826883080}{357911} a^{5} - \frac{12721887108413023679}{357911} a^{4} - \frac{30074690939633223515}{357911} a^{3} + \frac{53378064708045867711}{357911} a^{2} + \frac{9404525203112689179}{357911} a - \frac{8053791520133348024}{357911} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( -a^{4} + 5 a^{2} - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 5 a^{2} - 3\) , \( -164 a^{5} + 107 a^{4} + 1023 a^{3} - 299 a^{2} - 1427 a - 495\) , \( -1909 a^{5} + 1294 a^{4} + 11934 a^{3} - 3697 a^{2} - 16662 a - 5668\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+5a^{2}-3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(-164a^{5}+107a^{4}+1023a^{3}-299a^{2}-1427a-495\right){x}-1909a^{5}+1294a^{4}+11934a^{3}-3697a^{2}-16662a-5668$ |
| 71.1-a2 |
71.1-a |
$2$ |
$3$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71 \) |
$125.29298$ |
$(2a^5-3a^4-10a^3+12a^2+8a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$25332.57953$ |
2.86365 |
\( -\frac{24139675}{71} a^{5} - \frac{29399896}{71} a^{4} + \frac{86289125}{71} a^{3} + \frac{96183244}{71} a^{2} - \frac{4597239}{71} a - \frac{12480872}{71} \) |
\( \bigl[1\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 7 a - 2\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 9 a - 2\) , \( -30 a^{5} + 31 a^{4} + 174 a^{3} - 120 a^{2} - 210 a - 15\) , \( -101 a^{5} + 18 a^{4} + 681 a^{3} + 89 a^{2} - 1084 a - 625\bigr] \) |
${y}^2+{x}{y}+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+9a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+7a-2\right){x}^{2}+\left(-30a^{5}+31a^{4}+174a^{3}-120a^{2}-210a-15\right){x}-101a^{5}+18a^{4}+681a^{3}+89a^{2}-1084a-625$ |
| 71.1-b1 |
71.1-b |
$2$ |
$7$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( -71 \) |
$125.29298$ |
$(2a^5-3a^4-10a^3+12a^2+8a-2)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$0.516669825$ |
$54310.59746$ |
3.49572 |
\( -\frac{15041}{71} a^{5} + \frac{48771}{71} a^{4} - \frac{34465}{71} a^{3} - \frac{35773}{71} a^{2} + \frac{41060}{71} a + \frac{17902}{71} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} + a - 2\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 7 a - 3\) , \( a^{5} - 4 a^{3}\) , \( 4 a^{5} - 10 a^{4} - 17 a^{3} + 42 a^{2} + 3 a - 5\) , \( 13 a^{5} - 9 a^{4} - 58 a^{3} + 34 a^{2} + 13 a - 6\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}+a-2\right){x}{y}+\left(a^{5}-4a^{3}\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+7a-3\right){x}^{2}+\left(4a^{5}-10a^{4}-17a^{3}+42a^{2}+3a-5\right){x}+13a^{5}-9a^{4}-58a^{3}+34a^{2}+13a-6$ |
| 71.1-b2 |
71.1-b |
$2$ |
$7$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{7} \) |
$125.29298$ |
$(2a^5-3a^4-10a^3+12a^2+8a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$3.616688776$ |
$0.461632461$ |
3.49572 |
\( \frac{122468998322313866474000766681}{9095120158391} a^{5} + \frac{102223366445428868314235305639}{9095120158391} a^{4} - \frac{547269184906593646587878244836}{9095120158391} a^{3} - \frac{514188332840315863706847559229}{9095120158391} a^{2} + \frac{36383557027502587292508599169}{9095120158391} a + \frac{66752423214826896262582563915}{9095120158391} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 4 a\) , \( a^{3} + a^{2} - 5 a - 2\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 4 a - 2\) , \( -279 a^{5} + 194 a^{4} + 1813 a^{3} - 647 a^{2} - 2605 a - 876\) , \( -4405 a^{5} + 2861 a^{4} + 28211 a^{3} - 8918 a^{2} - 39799 a - 13522\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-4a\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+4a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(-279a^{5}+194a^{4}+1813a^{3}-647a^{2}-2605a-876\right){x}-4405a^{5}+2861a^{4}+28211a^{3}-8918a^{2}-39799a-13522$ |
*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.
