| 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 |
| 3.1-a1 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{3} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.386829285$ |
$1096.595045$ |
1.49360316 |
\( \frac{103260780444158037910828}{27} a^{4} - \frac{217382177374882773824560}{27} a^{3} - \frac{161936812364279481908756}{27} a^{2} + \frac{340905586007378298419960}{27} a - \frac{98101775469368714335592}{27} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( -a^{2} + 2\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 7\) , \( -19 a^{4} + 41 a^{3} + 21 a^{2} - 61 a + 20\) , \( 175 a^{4} - 364 a^{3} - 279 a^{2} + 581 a - 171\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-6a+7\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-19a^{4}+41a^{3}+21a^{2}-61a+20\right){x}+175a^{4}-364a^{3}-279a^{2}+581a-171$ |
| 3.1-a2 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.128943095$ |
$3289.785137$ |
1.49360316 |
\( -\frac{204133864169380}{3} a^{4} - \frac{166451407233128}{3} a^{3} + \frac{1089078174056084}{3} a^{2} + \frac{888037834457512}{3} a - \frac{500694288430936}{3} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{4} + a^{3} - 6 a^{2} - 4 a + 5\) , \( -3 a^{4} + 5 a^{3} + 10 a^{2} - 6 a - 4\) , \( -16 a^{4} + 34 a^{3} + 26 a^{2} - 49 a + 11\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-4a+5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(-3a^{4}+5a^{3}+10a^{2}-6a-4\right){x}-16a^{4}+34a^{3}+26a^{2}-49a+11$ |
| 3.1-a3 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.193414642$ |
$4386.380183$ |
1.49360316 |
\( \frac{9195375683888}{729} a^{4} - \frac{19172124711968}{729} a^{3} - \frac{14738593256128}{729} a^{2} + \frac{29941611793024}{729} a - \frac{8285926032832}{729} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 6 a + 9\) , \( a^{4} - 5 a^{2} + 3\) , \( 89 a^{4} + 70 a^{3} - 474 a^{2} - 375 a + 215\) , \( 209 a^{4} + 172 a^{3} - 1113 a^{2} - 918 a + 502\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-6a+9\right){x}^{2}+\left(89a^{4}+70a^{3}-474a^{2}-375a+215\right){x}+209a^{4}+172a^{3}-1113a^{2}-918a+502$ |
| 3.1-a4 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.064471547$ |
$13159.14055$ |
1.49360316 |
\( -\frac{38338768}{9} a^{4} - \frac{31168544}{9} a^{3} + \frac{204504128}{9} a^{2} + \frac{166349056}{9} a - \frac{93849664}{9} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{4} - 4 a^{2} + 1\) , \( a^{3} - 2 a^{2} - 6 a + 3\) , \( -a^{3} - a^{2} + 3 a - 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(a^{3}-2a^{2}-6a+3\right){x}-a^{3}-a^{2}+3a-1$ |
| 3.1-a5 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.032235773$ |
$6579.570275$ |
1.49360316 |
\( \frac{94976}{81} a^{4} + \frac{98176}{81} a^{3} - \frac{542080}{81} a^{2} - \frac{505472}{81} a + \frac{409856}{81} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( a^{4} - 4 a^{2} + 4 a\) , \( a^{3} + a^{2} - a\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(a^{4}-4a^{2}+4a\right){x}+a^{3}+a^{2}-a$ |
| 3.1-a6 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.128943095$ |
$3289.785137$ |
1.49360316 |
\( -\frac{802827356}{3} a^{4} + \frac{1075221992}{3} a^{3} + \frac{3414508012}{3} a^{2} - \frac{4554410536}{3} a + \frac{1215425224}{3} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 5 a + 6\) , \( -a^{4} - a^{3} + 7 a^{2} + 5 a - 7\) , \( 1\) , \( -6 a^{4} - a^{3} + 40 a^{2} + 15 a - 35\) , \( 20 a^{4} + 10 a^{3} - 111 a^{2} - 46 a + 96\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-5a+6\right){x}{y}+{y}={x}^{3}+\left(-a^{4}-a^{3}+7a^{2}+5a-7\right){x}^{2}+\left(-6a^{4}-a^{3}+40a^{2}+15a-35\right){x}+20a^{4}+10a^{3}-111a^{2}-46a+96$ |
| 3.1-a7 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.096707321$ |
$2193.190091$ |
1.49360316 |
\( -\frac{152022271483648}{531441} a^{4} + \frac{202577655160192}{531441} a^{3} + \frac{642171779561600}{531441} a^{2} - \frac{855694669315712}{531441} a + \frac{228145550464256}{531441} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( a^{4} - 4 a^{2} - 2 a - 1\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 5 a + 5\) , \( -21 a^{4} + 35 a^{3} + 45 a^{2} - 48 a + 7\) , \( 114 a^{4} - 234 a^{3} - 187 a^{2} + 360 a - 102\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){x}{y}+\left(2a^{4}+a^{3}-10a^{2}-5a+5\right){y}={x}^{3}+\left(a^{4}-4a^{2}-2a-1\right){x}^{2}+\left(-21a^{4}+35a^{3}+45a^{2}-48a+7\right){x}+114a^{4}-234a^{3}-187a^{2}+360a-102$ |
| 3.1-a8 |
3.1-a |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.386829285$ |
$1096.595045$ |
1.49360316 |
\( \frac{941614692977390804}{27} a^{4} + \frac{369159190799268784}{27} a^{3} - \frac{5504958087811966828}{27} a^{2} - \frac{2158209806856234872}{27} a + \frac{4803563953569624152}{27} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( -a^{2} + 2\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -18 a^{4} - 20 a^{3} + 56 a^{2} + 35 a - 44\) , \( 46 a^{4} + 142 a^{3} + 61 a^{2} - 116 a - 42\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-18a^{4}-20a^{3}+56a^{2}+35a-44\right){x}+46a^{4}+142a^{3}+61a^{2}-116a-42$ |
| 3.1-b1 |
3.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.007302084$ |
$17958.93179$ |
0.923478790 |
\( -\frac{4610560}{81} a^{4} + \frac{6119296}{81} a^{3} + \frac{19476608}{81} a^{2} - \frac{25864832}{81} a + \frac{6871808}{81} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -2 a^{4} - a^{3} + 12 a^{2} + 7 a - 8\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 3\) , \( -5 a^{4} - 4 a^{3} + 31 a^{2} + 24 a - 17\) , \( -a^{4} - 2 a^{3} + 7 a^{2} + 15 a + 6\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-4a+3\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+12a^{2}+7a-8\right){x}^{2}+\left(-5a^{4}-4a^{3}+31a^{2}+24a-17\right){x}-a^{4}-2a^{3}+7a^{2}+15a+6$ |
| 3.1-b2 |
3.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.014604168$ |
$35917.86359$ |
0.923478790 |
\( \frac{2395568}{9} a^{4} + \frac{2599840}{9} a^{3} - \frac{8494720}{9} a^{2} - \frac{4851584}{9} a + \frac{7233344}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( -a^{3} + 4 a - 2\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( -a^{3} - a^{2} + 2 a - 1\) , \( 5 a^{3} + 4 a^{2} - 12 a + 4\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){y}={x}^{3}+\left(-a^{3}+4a-2\right){x}^{2}+\left(-a^{3}-a^{2}+2a-1\right){x}+5a^{3}+4a^{2}-12a+4$ |
| 3.1-b3 |
3.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.029208336$ |
$8979.465898$ |
0.923478790 |
\( \frac{208092930164}{3} a^{4} + \frac{56223228184}{3} a^{3} - \frac{1173129707428}{3} a^{2} - \frac{420154245104}{3} a + \frac{1000115800280}{3} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 5 a + 8\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a + 5\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 5 a + 5\) , \( -73 a^{4} - 27 a^{3} + 425 a^{2} + 159 a - 364\) , \( 302 a^{4} + 119 a^{3} - 1765 a^{2} - 696 a + 1536\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-5a+8\right){x}{y}+\left(2a^{4}+a^{3}-10a^{2}-5a+5\right){y}={x}^{3}+\left(2a^{4}+a^{3}-10a^{2}-6a+5\right){x}^{2}+\left(-73a^{4}-27a^{3}+425a^{2}+159a-364\right){x}+302a^{4}+119a^{3}-1765a^{2}-696a+1536$ |
| 3.1-b4 |
3.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$35.40716$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.029208336$ |
$8979.465898$ |
0.923478790 |
\( \frac{1646672929420}{3} a^{4} + \frac{3672610185320}{3} a^{3} - \frac{1689099685340}{3} a^{2} - \frac{3767733486736}{3} a + \frac{1476543386776}{3} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 6\) , \( -a^{4} - a^{3} + 6 a^{2} + 6 a - 5\) , \( a^{4} + a^{3} - 6 a^{2} - 4 a + 5\) , \( -4 a^{4} + 9 a^{3} + 4 a^{2} - 8 a - 2\) , \( 4 a^{4} - 8 a^{3} - 10 a^{2} + 21 a - 8\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+6\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-4a+5\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+6a-5\right){x}^{2}+\left(-4a^{4}+9a^{3}+4a^{2}-8a-2\right){x}+4a^{4}-8a^{3}-10a^{2}+21a-8$ |
| 4.1-a1 |
4.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$36.44055$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1610.699868$ |
1.13426418 |
\( 20949184560 a^{4} - 44103327704 a^{3} - 32851116216 a^{2} + 69165907912 a - 19904396416 \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( -2 a^{4} - a^{3} + 11 a^{2} + 5 a - 6\) , \( 0\) , \( -6 a^{4} + 8 a^{3} + 19 a^{2} - 18 a + 5\) , \( -14 a^{4} + 26 a^{3} + 31 a^{2} - 49 a + 13\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}={x}^{3}+\left(-2a^{4}-a^{3}+11a^{2}+5a-6\right){x}^{2}+\left(-6a^{4}+8a^{3}+19a^{2}-18a+5\right){x}-14a^{4}+26a^{3}+31a^{2}-49a+13$ |
| 4.1-a2 |
4.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$36.44055$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$6442.799474$ |
1.13426418 |
\( 45632 a^{4} - 29952 a^{3} - 75712 a^{2} + 59136 a + 512 \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( a^{4} - 6 a^{2} - a + 4\) , \( a^{4} - 5 a^{2} - a + 2\) , \( 9 a^{4} + 7 a^{3} - 49 a^{2} - 38 a + 26\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 6\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-6a^{2}-a+4\right){x}^{2}+\left(9a^{4}+7a^{3}-49a^{2}-38a+26\right){x}+2a^{4}+a^{3}-11a^{2}-6a+6$ |
| 4.1-a3 |
4.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$36.44055$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6442.799474$ |
1.13426418 |
\( 33324064 a^{4} + 13078432 a^{3} - 194835584 a^{2} - 76443584 a + 170054400 \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( -a^{3} + 4 a - 1\) , \( a^{2} - 2\) , \( a^{4} - 8 a^{2} - 4 a + 9\) , \( -a^{4} - 2 a^{3} + a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(a^{4}-8a^{2}-4a+9\right){x}-a^{4}-2a^{3}+a^{2}+2a-1$ |
| 4.1-a4 |
4.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$36.44055$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$402.6749671$ |
1.13426418 |
\( 7578578864 a^{4} + 16902553656 a^{3} - 7775043272 a^{2} - 17342087176 a + 6796411472 \) |
\( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 6\) , \( 0\) , \( 3 a^{4} - 6 a^{3} - 13 a^{2} + 26 a - 5\) , \( 8 a^{4} - 9 a^{3} - 36 a^{2} + 38 a - 8\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(2a^{4}+a^{3}-11a^{2}-6a+6\right){x}^{2}+\left(3a^{4}-6a^{3}-13a^{2}+26a-5\right){x}+8a^{4}-9a^{3}-36a^{2}+38a-8$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{17} \cdot 3 \) |
$37.94845$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$451.6265196$ |
1.27215205 |
\( -\frac{368279}{48} a^{4} - \frac{430063}{48} a^{3} + \frac{72125}{6} a^{2} + \frac{95213}{12} a - \frac{62779}{6} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 5\) , \( -a^{3} + 4 a - 2\) , \( a^{4} - 4 a^{2} + 1\) , \( -9 a^{4} - 2 a^{3} + 52 a^{2} + 12 a - 44\) , \( 19 a^{4} + 6 a^{3} - 112 a^{2} - 38 a + 96\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+5\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-a^{3}+4a-2\right){x}^{2}+\left(-9a^{4}-2a^{3}+52a^{2}+12a-44\right){x}+19a^{4}+6a^{3}-112a^{2}-38a+96$ |
| 6.1-b1 |
6.1-b |
$2$ |
$3$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3^{3} \) |
$37.94845$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 5 \) |
$1$ |
$115.5378248$ |
1.62724812 |
\( -\frac{11666657018}{27} a^{4} + \frac{49122785023}{54} a^{3} + \frac{18294698815}{27} a^{2} - \frac{38519018965}{27} a + \frac{22169965187}{54} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a + 5\) , \( a^{4} - 5 a^{2} + 3\) , \( -a^{4} - 3 a^{3} + 7 a^{2} + 14 a - 7\) , \( 52 a^{4} - 68 a^{3} - 221 a^{2} + 288 a - 77\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(2a^{4}+a^{3}-10a^{2}-6a+5\right){x}^{2}+\left(-a^{4}-3a^{3}+7a^{2}+14a-7\right){x}+52a^{4}-68a^{3}-221a^{2}+288a-77$ |
| 6.1-b2 |
6.1-b |
$2$ |
$3$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3^{9} \) |
$37.94845$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$38.51260827$ |
1.62724812 |
\( \frac{1217518564472586425}{39366} a^{4} + \frac{3971074157390073181}{157464} a^{3} - \frac{3247802369135552222}{19683} a^{2} - \frac{2648268460264967833}{19683} a + \frac{11945192830698762167}{157464} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 5 a + 5\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 5 a + 10\) , \( a^{4} - 5 a^{2} - a + 2\) , \( a^{3} + 3 a^{2} - 2 a - 8\) , \( -31 a^{4} - 9 a^{3} + 186 a^{2} + 60 a - 174\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-5a+5\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-5a+10\right){x}^{2}+\left(a^{3}+3a^{2}-2a-8\right){x}-31a^{4}-9a^{3}+186a^{2}+60a-174$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{8} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.026523259$ |
$6810.721358$ |
2.54419037 |
\( -212299600 a^{4} - 173178824 a^{3} + 1133067272 a^{2} + 924057256 a - 520976816 \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( -2 a^{4} - a^{3} + 12 a^{2} + 6 a - 9\) , \( a^{4} - 5 a^{2} + 2\) , \( -18 a^{4} + 28 a^{3} + 44 a^{2} - 36 a - 2\) , \( -114 a^{4} + 239 a^{3} + 179 a^{2} - 372 a + 108\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+12a^{2}+6a-9\right){x}^{2}+\left(-18a^{4}+28a^{3}+44a^{2}-36a-2\right){x}-114a^{4}+239a^{3}+179a^{2}-372a+108$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.053046519$ |
$27242.88543$ |
2.54419037 |
\( 95552 a^{4} + 34560 a^{3} - 562368 a^{2} - 204800 a + 508928 \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 7 a + 8\) , \( a\) , \( 3 a^{4} + a^{3} - 19 a^{2} - 7 a + 20\) , \( 3 a^{4} + 2 a^{3} - 19 a^{2} - 9 a + 17\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){x}{y}+a{y}={x}^{3}+\left(2a^{4}+a^{3}-11a^{2}-7a+8\right){x}^{2}+\left(3a^{4}+a^{3}-19a^{2}-7a+20\right){x}+3a^{4}+2a^{3}-19a^{2}-9a+17$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.026523259$ |
$6810.721358$ |
2.54419037 |
\( -357600 a^{4} + 479136 a^{3} + 1515776 a^{2} - 2014656 a + 536320 \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( a^{4} - 4 a^{2}\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( 6 a^{4} - 6 a^{3} - 22 a^{2} + 26 a - 11\) , \( -23 a^{4} + 31 a^{3} + 101 a^{2} - 130 a + 30\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){y}={x}^{3}+\left(a^{4}-4a^{2}\right){x}^{2}+\left(6a^{4}-6a^{3}-22a^{2}+26a-11\right){x}-23a^{4}+31a^{3}+101a^{2}-130a+30$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.026523259$ |
$6810.721358$ |
2.54419037 |
\( 35677900848 a^{4} + 13987455016 a^{3} - 208583639304 a^{2} - 81774854376 a + 182007726976 \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( a^{4} - 6 a^{2} - a + 3\) , \( a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( -8 a^{4} - 7 a^{3} + 43 a^{2} + 38 a - 17\) , \( -356 a^{4} - 291 a^{3} + 1898 a^{2} + 1551 a - 870\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){y}={x}^{3}+\left(a^{4}-6a^{2}-a+3\right){x}^{2}+\left(-8a^{4}-7a^{3}+43a^{2}+38a-17\right){x}-356a^{4}-291a^{3}+1898a^{2}+1551a-870$ |
| 8.1-b1 |
8.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$814.4246240$ |
1.14704508 |
\( 472982816074080 a^{4} - 995712350688760 a^{3} - 741746567943240 a^{2} + 1561507508946264 a - 449352152972320 \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( -22 a^{4} + 52 a^{3} + 41 a^{2} - 78 a + 16\) , \( 202 a^{4} - 416 a^{3} - 304 a^{2} + 660 a - 202\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){x}^{2}+\left(-22a^{4}+52a^{3}+41a^{2}-78a+16\right){x}+202a^{4}-416a^{3}-304a^{2}+660a-202$ |
| 8.1-b2 |
8.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$814.4246240$ |
1.14704508 |
\( -439500512 a^{4} - 356980320 a^{3} + 2348962304 a^{2} + 1913869376 a - 1079495680 \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( -a^{4} - a^{3} + 6 a^{2} + 4 a - 6\) , \( a^{2} - 2\) , \( -48 a^{4} - 18 a^{3} + 282 a^{2} + 104 a - 253\) , \( -265 a^{4} - 102 a^{3} + 1551 a^{2} + 598 a - 1363\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+4a-6\right){x}^{2}+\left(-48a^{4}-18a^{3}+282a^{2}+104a-253\right){x}-265a^{4}-102a^{3}+1551a^{2}+598a-1363$ |
| 8.1-b3 |
8.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$3257.698496$ |
1.14704508 |
\( 143633472 a^{4} + 45319424 a^{3} - 820905664 a^{2} - 304580096 a + 706137088 \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -a^{3} + 5 a - 2\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -134 a^{4} - 51 a^{3} + 780 a^{2} + 301 a - 670\) , \( -1102 a^{4} - 434 a^{3} + 6443 a^{2} + 2535 a - 5623\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{3}+5a-2\right){x}^{2}+\left(-134a^{4}-51a^{3}+780a^{2}+301a-670\right){x}-1102a^{4}-434a^{3}+6443a^{2}+2535a-5623$ |
| 8.1-b4 |
8.1-b |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{8} \) |
$39.05602$ |
$(a^4-5a^2-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$814.4246240$ |
1.14704508 |
\( 64981928429719936 a^{4} + 25476048505355352 a^{3} - 379903731449332152 a^{2} - 148940576613333400 a + 331499684620042480 \) |
\( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 5 a + 7\) , \( a^{4} - 5 a^{2} + 2\) , \( 10 a^{4} + 9 a^{3} - 59 a^{2} - 52 a + 36\) , \( -19 a^{4} - 19 a^{3} + 105 a^{2} + 102 a - 52\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(2a^{4}+a^{3}-11a^{2}-5a+7\right){x}^{2}+\left(10a^{4}+9a^{3}-59a^{2}-52a+36\right){x}-19a^{4}-19a^{3}+105a^{2}+102a-52$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1003.910259$ |
2.82783769 |
\( -\frac{4610560}{81} a^{4} + \frac{6119296}{81} a^{3} + \frac{19476608}{81} a^{2} - \frac{25864832}{81} a + \frac{6871808}{81} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 5 a + 8\) , \( a + 1\) , \( 3 a^{4} + a^{3} - 19 a^{2} - 7 a + 19\) , \( 4 a^{4} + 3 a^{3} - 26 a^{2} - 13 a + 23\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-5a+8\right){x}^{2}+\left(3a^{4}+a^{3}-19a^{2}-7a+19\right){x}+4a^{4}+3a^{3}-26a^{2}-13a+23$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4015.641038$ |
2.82783769 |
\( \frac{2395568}{9} a^{4} + \frac{2599840}{9} a^{3} - \frac{8494720}{9} a^{2} - \frac{4851584}{9} a + \frac{7233344}{9} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( a^{3} - 4 a + 2\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 7\) , \( -3 a^{4} + 8 a^{3} + 22 a^{2} - 35 a - 37\) , \( -2 a^{4} - 11 a^{3} - 6 a^{2} + 56 a + 81\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-6a+7\right){y}={x}^{3}+\left(a^{3}-4a+2\right){x}^{2}+\left(-3a^{4}+8a^{3}+22a^{2}-35a-37\right){x}-2a^{4}-11a^{3}-6a^{2}+56a+81$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1003.910259$ |
2.82783769 |
\( \frac{208092930164}{3} a^{4} + \frac{56223228184}{3} a^{3} - \frac{1173129707428}{3} a^{2} - \frac{420154245104}{3} a + \frac{1000115800280}{3} \) |
\( \bigl[a\) , \( a^{4} + a^{3} - 7 a^{2} - 6 a + 6\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 5 a + 5\) , \( -55 a^{4} - 20 a^{3} + 317 a^{2} + 119 a - 269\) , \( 226 a^{4} + 91 a^{3} - 1323 a^{2} - 527 a + 1155\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{4}+a^{3}-10a^{2}-5a+5\right){y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-6a+6\right){x}^{2}+\left(-55a^{4}-20a^{3}+317a^{2}+119a-269\right){x}+226a^{4}+91a^{3}-1323a^{2}-527a+1155$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{7} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2007.820519$ |
2.82783769 |
\( \frac{1646672929420}{3} a^{4} + \frac{3672610185320}{3} a^{3} - \frac{1689099685340}{3} a^{2} - \frac{3767733486736}{3} a + \frac{1476543386776}{3} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{3} + 2 a^{2} + 4 a - 6\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( -60 a^{4} + 132 a^{3} + 85 a^{2} - 208 a + 65\) , \( -121 a^{4} + 250 a^{3} + 199 a^{2} - 400 a + 111\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-6\right){x}^{2}+\left(-60a^{4}+132a^{3}+85a^{2}-208a+65\right){x}-121a^{4}+250a^{3}+199a^{2}-400a+111$ |
| 9.1-b1 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$80.01205497$ |
1.01420915 |
\( \frac{103260780444158037910828}{27} a^{4} - \frac{217382177374882773824560}{27} a^{3} - \frac{161936812364279481908756}{27} a^{2} + \frac{340905586007378298419960}{27} a - \frac{98101775469368714335592}{27} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -a^{4} - a^{3} + 7 a^{2} + 5 a - 6\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 3\) , \( 241 a^{4} + 223 a^{3} - 1257 a^{2} - 1172 a + 436\) , \( 3865 a^{4} + 3267 a^{3} - 20501 a^{2} - 17357 a + 8818\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-5a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+7a^{2}+5a-6\right){x}^{2}+\left(241a^{4}+223a^{3}-1257a^{2}-1172a+436\right){x}+3865a^{4}+3267a^{3}-20501a^{2}-17357a+8818$ |
| 9.1-b2 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3240.488226$ |
1.01420915 |
\( -\frac{204133864169380}{3} a^{4} - \frac{166451407233128}{3} a^{3} + \frac{1089078174056084}{3} a^{2} + \frac{888037834457512}{3} a - \frac{500694288430936}{3} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 5 a + 8\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 7 a + 10\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 3\) , \( 7 a^{4} + 5 a^{3} - 42 a^{2} - 26 a + 32\) , \( -21 a^{4} - 10 a^{3} + 122 a^{2} + 55 a - 101\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-5a+8\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-7a+10\right){x}^{2}+\left(7a^{4}+5a^{3}-42a^{2}-26a+32\right){x}-21a^{4}-10a^{3}+122a^{2}+55a-101$ |
| 9.1-b3 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$160.0241099$ |
1.01420915 |
\( \frac{9195375683888}{729} a^{4} - \frac{19172124711968}{729} a^{3} - \frac{14738593256128}{729} a^{2} + \frac{29941611793024}{729} a - \frac{8285926032832}{729} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( -a^{4} + 5 a^{2} + a - 3\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 5 a + 7\) , \( 8 a^{4} + 10 a^{3} - 43 a^{2} - 42 a + 15\) , \( 14 a^{4} + 14 a^{3} - 76 a^{2} - 63 a + 30\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-5a+7\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+a-3\right){x}^{2}+\left(8a^{4}+10a^{3}-43a^{2}-42a+15\right){x}+14a^{4}+14a^{3}-76a^{2}-63a+30$ |
| 9.1-b4 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$12961.95290$ |
1.01420915 |
\( -\frac{38338768}{9} a^{4} - \frac{31168544}{9} a^{3} + \frac{204504128}{9} a^{2} + \frac{166349056}{9} a - \frac{93849664}{9} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 6\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a + 5\) , \( a^{4} + 4 a^{3} - 9 a^{2} - 16 a + 10\) , \( -a^{4} + 3 a^{3} + a^{2} - 8 a + 3\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(2a^{4}+a^{3}-10a^{2}-6a+5\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-5a+6\right){x}^{2}+\left(a^{4}+4a^{3}-9a^{2}-16a+10\right){x}-a^{4}+3a^{3}+a^{2}-8a+3$ |
| 9.1-b5 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3240.488226$ |
1.01420915 |
\( \frac{94976}{81} a^{4} + \frac{98176}{81} a^{3} - \frac{542080}{81} a^{2} - \frac{505472}{81} a + \frac{409856}{81} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( a^{3} - a^{2} - 4 a + 4\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 3\) , \( 2 a^{4} + 3 a^{3} - 10 a^{2} - 13 a + 10\) , \( 2 a^{4} + 5 a^{3} - 3 a^{2} - 8 a + 5\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-4a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+4\right){x}^{2}+\left(2a^{4}+3a^{3}-10a^{2}-13a+10\right){x}+2a^{4}+5a^{3}-3a^{2}-8a+5$ |
| 9.1-b6 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{7} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$6480.976453$ |
1.01420915 |
\( -\frac{802827356}{3} a^{4} + \frac{1075221992}{3} a^{3} + \frac{3414508012}{3} a^{2} - \frac{4554410536}{3} a + \frac{1215425224}{3} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 5 a + 8\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 7 a + 10\) , \( a^{4} - 4 a^{2} + 1\) , \( 4 a^{4} + 4 a^{3} - 32 a^{2} - 17 a + 30\) , \( 12 a^{3} - 13 a^{2} - 22 a + 20\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-5a+8\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-7a+10\right){x}^{2}+\left(4a^{4}+4a^{3}-32a^{2}-17a+30\right){x}+12a^{3}-13a^{2}-22a+20$ |
| 9.1-b7 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$40.00602748$ |
1.01420915 |
\( -\frac{152022271483648}{531441} a^{4} + \frac{202577655160192}{531441} a^{3} + \frac{642171779561600}{531441} a^{2} - \frac{855694669315712}{531441} a + \frac{228145550464256}{531441} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( a^{2} - 1\) , \( -607 a^{4} - 239 a^{3} + 3548 a^{2} + 1394 a - 3094\) , \( -10798 a^{4} - 4234 a^{3} + 63128 a^{2} + 24751 a - 55084\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-4\right){x}^{2}+\left(-607a^{4}-239a^{3}+3548a^{2}+1394a-3094\right){x}-10798a^{4}-4234a^{3}+63128a^{2}+24751a-55084$ |
| 9.1-b8 |
9.1-b |
$8$ |
$12$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$39.51875$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$40.00602748$ |
1.01420915 |
\( \frac{941614692977390804}{27} a^{4} + \frac{369159190799268784}{27} a^{3} - \frac{5504958087811966828}{27} a^{2} - \frac{2158209806856234872}{27} a + \frac{4803563953569624152}{27} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 6\) , \( -2 a^{4} - a^{3} + 12 a^{2} + 5 a - 10\) , \( 1\) , \( -133 a^{4} - 40 a^{3} + 756 a^{2} + 277 a - 648\) , \( -850 a^{4} - 349 a^{3} + 4934 a^{2} + 2171 a - 4486\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+6\right){x}{y}+{y}={x}^{3}+\left(-2a^{4}-a^{3}+12a^{2}+5a-10\right){x}^{2}+\left(-133a^{4}-40a^{3}+756a^{2}+277a-648\right){x}-850a^{4}-349a^{3}+4934a^{2}+2171a-4486$ |
| 12.1-a1 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{24} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \cdot 3 \) |
$1$ |
$19.45130117$ |
1.31498102 |
\( -\frac{104519690793417168546369598}{282429536481} a^{4} - \frac{85225690602650260401616346}{282429536481} a^{3} + \frac{557624843628477220537364276}{282429536481} a^{2} + \frac{454689083158852005520889296}{282429536481} a - \frac{256363209762402109742287420}{282429536481} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( 0\) , \( -86 a^{4} + 187 a^{3} + 142 a^{2} - 291 a + 77\) , \( -1670 a^{4} + 3679 a^{3} + 2642 a^{2} - 5723 a + 1652\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(-86a^{4}+187a^{3}+142a^{2}-291a+77\right){x}-1670a^{4}+3679a^{3}+2642a^{2}-5723a+1652$ |
| 12.1-a2 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{8} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \) |
$1$ |
$58.35390351$ |
1.31498102 |
\( \frac{5521852822675849142}{6561} a^{4} - \frac{11624475281253683402}{6561} a^{3} - \frac{8659543735059299464}{6561} a^{2} + \frac{18229868730595545136}{6561} a - \frac{5245975902215213116}{6561} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( a^{4} - 6 a^{2} - a + 5\) , \( a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( 15 a^{4} + 9 a^{3} - 84 a^{2} - 60 a + 39\) , \( 27 a^{4} - 15 a^{3} - 253 a^{2} - 165 a + 103\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){y}={x}^{3}+\left(a^{4}-6a^{2}-a+5\right){x}^{2}+\left(15a^{4}+9a^{3}-84a^{2}-60a+39\right){x}+27a^{4}-15a^{3}-253a^{2}-165a+103$ |
| 12.1-a3 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3 \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$7469.299650$ |
1.31498102 |
\( -\frac{505020887104}{3} a^{4} - \frac{411795529784}{3} a^{3} + \frac{2694345769352}{3} a^{2} + \frac{2196977664184}{3} a - \frac{1238702012512}{3} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( a^{3} - 5 a + 1\) , \( a^{4} - 4 a^{2}\) , \( 109 a^{4} + 47 a^{3} - 635 a^{2} - 266 a + 553\) , \( 601 a^{4} + 235 a^{3} - 3513 a^{2} - 1367 a + 3079\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){x}{y}+\left(a^{4}-4a^{2}\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(109a^{4}+47a^{3}-635a^{2}-266a+553\right){x}+601a^{4}+235a^{3}-3513a^{2}-1367a+3079$ |
| 12.1-a4 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$933.6624562$ |
1.31498102 |
\( \frac{473065760}{81} a^{4} - \frac{995375672}{81} a^{3} - \frac{736216792}{81} a^{2} + \frac{1547745112}{81} a - \frac{441873424}{81} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( a^{4} - 5 a^{2} - 2 a + 3\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( -235 a^{4} - 93 a^{3} + 1376 a^{2} + 540 a - 1204\) , \( -2974 a^{4} - 1167 a^{3} + 17387 a^{2} + 6818 a - 15173\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){y}={x}^{3}+\left(a^{4}-5a^{2}-2a+3\right){x}^{2}+\left(-235a^{4}-93a^{3}+1376a^{2}+540a-1204\right){x}-2974a^{4}-1167a^{3}+17387a^{2}+6818a-15173$ |
| 12.1-a5 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$14938.59930$ |
1.31498102 |
\( -\frac{1895872}{9} a^{4} - \frac{1558784}{9} a^{3} + \frac{10128704}{9} a^{2} + \frac{8283904}{9} a - \frac{4641280}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{4} - 2 a^{3} + 7 a^{2} + 5 a - 6\) , \( -2 a^{3} + 2 a^{2} + 5 a - 3\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{4}-2a^{3}+7a^{2}+5a-6\right){x}-2a^{3}+2a^{2}+5a-3$ |
| 12.1-a6 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$7469.299650$ |
1.31498102 |
\( \frac{3167968}{3} a^{4} + \frac{1340000}{3} a^{3} - \frac{18267008}{3} a^{2} - \frac{7265344}{3} a + \frac{15941632}{3} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -2 a^{4} - a^{3} + 11 a^{2} + 6 a - 8\) , \( a^{2} - 2\) , \( 3 a^{4} + 2 a^{3} - 18 a^{2} - 12 a + 12\) , \( -15 a^{4} - 12 a^{3} + 80 a^{2} + 64 a - 38\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+11a^{2}+6a-8\right){x}^{2}+\left(3a^{4}+2a^{3}-18a^{2}-12a+12\right){x}-15a^{4}-12a^{3}+80a^{2}+64a-38$ |
| 12.1-a7 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4979.533100$ |
1.31498102 |
\( \frac{6206721344}{729} a^{4} + \frac{32627626240}{729} a^{3} + \frac{5871083840}{729} a^{2} - \frac{61985083136}{729} a + \frac{26211499520}{729} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 4 a + 6\) , \( -a^{4} + 6 a^{2} + a - 3\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 6\) , \( -15 a^{4} - 29 a^{3} + 28 a^{2} + 33 a - 28\) , \( 83 a^{4} + 190 a^{3} - 72 a^{2} - 192 a + 58\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-4a+6\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+6\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-3\right){x}^{2}+\left(-15a^{4}-29a^{3}+28a^{2}+33a-28\right){x}+83a^{4}+190a^{3}-72a^{2}-192a+58$ |
| 12.1-a8 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \) |
$1$ |
$58.35390351$ |
1.31498102 |
\( -\frac{158321152166}{9} a^{4} + \frac{229088535770}{9} a^{3} + \frac{674203785160}{9} a^{2} - \frac{945496144816}{9} a + \frac{268483472620}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 5 a + 6\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 6 a + 8\) , \( a^{2} + a - 2\) , \( -31 a^{4} - 35 a^{3} + 161 a^{2} + 171 a - 76\) , \( -49 a^{4} - 67 a^{3} + 232 a^{2} + 273 a - 131\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-5a+6\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(2a^{4}+a^{3}-11a^{2}-6a+8\right){x}^{2}+\left(-31a^{4}-35a^{3}+161a^{2}+171a-76\right){x}-49a^{4}-67a^{3}+232a^{2}+273a-131$ |
| 12.1-a9 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{12} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$311.2208187$ |
1.31498102 |
\( \frac{7237069058700312560}{531441} a^{4} + \frac{2837277714402708808}{531441} a^{3} - \frac{42310066532820310072}{531441} a^{2} - \frac{16587573799034940008}{531441} a + \frac{36919295508519511376}{531441} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( -a^{4} - a^{3} + 6 a^{2} + 5 a - 6\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -49 a^{4} + 104 a^{3} + 73 a^{2} - 158 a + 43\) , \( 11 a^{4} - 22 a^{3} - 15 a^{2} + 23 a - 7\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+5a-6\right){x}^{2}+\left(-49a^{4}+104a^{3}+73a^{2}-158a+43\right){x}+11a^{4}-22a^{3}-15a^{2}+23a-7$ |
| 12.1-a10 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{3} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$2489.766550$ |
1.31498102 |
\( -\frac{18907118442234928}{27} a^{4} + \frac{25194153955618696}{27} a^{3} + \frac{79871002126068968}{27} a^{2} - \frac{106430083181406536}{27} a + \frac{28377910818909824}{27} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 2\) , \( a^{4} - 4 a^{2}\) , \( 77 a^{4} + 80 a^{3} - 430 a^{2} - 374 a + 205\) , \( -585 a^{4} - 552 a^{3} + 3225 a^{2} + 2745 a - 1526\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){x}{y}+\left(a^{4}-4a^{2}\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-5a+2\right){x}^{2}+\left(77a^{4}+80a^{3}-430a^{2}-374a+205\right){x}-585a^{4}-552a^{3}+3225a^{2}+2745a-1526$ |
| 12.1-a11 |
12.1-a |
$12$ |
$24$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{3} \) |
$40.67215$ |
$(a^4-5a^2-a+2), (-a^4+5a^2+a-3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$2489.766550$ |
1.31498102 |
\( \frac{236765389887608032}{27} a^{4} + \frac{528046339227269216}{27} a^{3} - \frac{242916258781234304}{27} a^{2} - \frac{541764323109004864}{27} a + \frac{212321706199750912}{27} \) |
\( \bigl[2 a^{4} + a^{3} - 10 a^{2} - 6 a + 6\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 4\) , \( -8 a^{4} - 3 a^{3} + 41 a^{2} + 22 a - 27\) , \( -a^{4} - 20 a^{3} + 34 a^{2} + 49 a - 39\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-10a^{2}-6a+6\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-4a+4\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+a-1\right){x}^{2}+\left(-8a^{4}-3a^{3}+41a^{2}+22a-27\right){x}-a^{4}-20a^{3}+34a^{2}+49a-39$ |
*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.
