| 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 |
| 4.1-a1 |
4.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{36} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$13.76668191$ |
1.59091870 |
\( -\frac{2239153498933929}{262144} a^{4} + \frac{1851481866191337}{262144} a^{3} + \frac{5564308702503739}{131072} a^{2} + \frac{4098775115398833}{262144} a - \frac{238603097358801}{32768} \) |
\( \bigl[-a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 3\) , \( -8 a^{4} + 25 a^{3} + 5 a^{2} - 29 a - 21\) , \( -47 a^{4} + 144 a^{3} + 29 a^{2} - 156 a - 67\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a+1\right){x}^{2}+\left(-8a^{4}+25a^{3}+5a^{2}-29a-21\right){x}-47a^{4}+144a^{3}+29a^{2}-156a-67$ |
| 4.1-a2 |
4.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{12} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3345.303705$ |
1.59091870 |
\( -\frac{2939}{4} a^{4} + \frac{72833}{64} a^{3} + \frac{223319}{64} a^{2} - \frac{11423}{32} a - \frac{1289}{64} \) |
\( \bigl[-a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 3\) , \( 2 a^{4} - 5 a^{3} - 5 a^{2} + 6 a + 4\) , \( a^{4} - 3 a^{3} + a - 1\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a+1\right){x}^{2}+\left(2a^{4}-5a^{3}-5a^{2}+6a+4\right){x}+a^{4}-3a^{3}+a-1$ |
| 4.1-a3 |
4.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6690.607410$ |
1.59091870 |
\( \frac{17575}{8} a^{4} - \frac{15219}{4} a^{3} - \frac{77171}{8} a^{2} + \frac{43307}{8} a + \frac{75383}{8} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a\) , \( a\) , \( -7 a^{4} + 12 a^{3} + 28 a^{2} - 14 a - 10\) , \( -10 a^{4} + 15 a^{3} + 48 a^{2} - 18 a - 38\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+8a\right){x}^{2}+\left(-7a^{4}+12a^{3}+28a^{2}-14a-10\right){x}-10a^{4}+15a^{3}+48a^{2}-18a-38$ |
| 4.1-a4 |
4.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$27.53336383$ |
1.59091870 |
\( \frac{100820038903217}{512} a^{4} - \frac{174675047047081}{512} a^{3} - \frac{225038748394199}{256} a^{2} + \frac{283102989950999}{512} a + \frac{5912136677519}{8} \) |
\( \bigl[-a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{4} - 12 a^{3} - 2 a^{2} + 19 a - 10\) , \( -24 a^{4} - 46 a^{3} + 42 a^{2} + 66 a - 29\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a\right){x}^{2}+\left(a^{4}-12a^{3}-2a^{2}+19a-10\right){x}-24a^{4}-46a^{3}+42a^{2}+66a-29$ |
| 4.1-b1 |
4.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$293.4760377$ |
1.67481302 |
\( -\frac{408111022369}{4} a^{4} + \frac{368642752811}{2} a^{3} + \frac{2816957219861}{4} a^{2} + \frac{965407407075}{4} a - \frac{469784065645}{4} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 7 a - 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -4 a^{4} + 13 a^{3} - 12 a^{2} - 8 a + 12\) , \( -9 a^{4} - 15 a^{3} + 105 a^{2} - 14 a - 87\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(-2a^{4}+4a^{3}+7a^{2}-7a-4\right){x}^{2}+\left(-4a^{4}+13a^{3}-12a^{2}-8a+12\right){x}-9a^{4}-15a^{3}+105a^{2}-14a-87$ |
| 4.1-b2 |
4.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$2347.808302$ |
1.67481302 |
\( -110710 a^{4} + \frac{2246161}{16} a^{3} + \frac{10371335}{16} a^{2} + \frac{1945009}{8} a - \frac{1285401}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 7 a - 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -4 a^{4} + 8 a^{3} + 13 a^{2} - 13 a - 8\) , \( -2 a^{3} + 4 a^{2} + 4 a - 7\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(-2a^{4}+4a^{3}+7a^{2}-7a-4\right){x}^{2}+\left(-4a^{4}+8a^{3}+13a^{2}-13a-8\right){x}-2a^{3}+4a^{2}+4a-7$ |
| 4.1-b3 |
4.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2347.808302$ |
1.67481302 |
\( 988512 a^{4} - \frac{3434681}{2} a^{3} - \frac{8802317}{2} a^{2} + 2787767 a + \frac{7377425}{2} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 5 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} + a\) , \( -a^{4} + 7 a^{2} + 6 a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-2a^{4}+4a^{3}+7a^{2}-5a-2\right){x}^{2}+\left(-2a^{4}+3a^{3}+8a^{2}+a\right){x}-a^{4}+7a^{2}+6a-3$ |
| 4.1-b4 |
4.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$4695.616604$ |
1.67481302 |
\( -\frac{273430915}{4} a^{4} + \frac{381106647}{2} a^{3} + \frac{493413695}{4} a^{2} - \frac{1482335675}{4} a + \frac{347187397}{4} \) |
\( \bigl[a^{2} - 2 a\) , \( 2 a^{4} - 4 a^{3} - 7 a^{2} + 7 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} - a + 3\) , \( -7 a^{4} + 26 a^{3} - 12 a^{2} - 20 a + 10\) , \( -35 a^{4} + 123 a^{3} - 41 a^{2} - 91 a + 25\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}-a+3\right){y}={x}^{3}+\left(2a^{4}-4a^{3}-7a^{2}+7a+2\right){x}^{2}+\left(-7a^{4}+26a^{3}-12a^{2}-20a+10\right){x}-35a^{4}+123a^{3}-41a^{2}-91a+25$ |
| 4.1-b5 |
4.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$293.4760377$ |
1.67481302 |
\( \frac{62987866585}{256} a^{4} - \frac{54588173885}{128} a^{3} - \frac{281069705341}{256} a^{2} + \frac{176987806125}{256} a + \frac{236167680673}{256} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( a^{2} - 2 a\) , \( -3 a^{4} + 8 a^{3} + 6 a^{2} - 16 a + 4\) , \( 19 a^{4} - 53 a^{3} - 35 a^{2} + 105 a - 25\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(-3a^{4}+8a^{3}+6a^{2}-16a+4\right){x}+19a^{4}-53a^{3}-35a^{2}+105a-25$ |
| 4.1-b6 |
4.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$586.9520755$ |
1.67481302 |
\( -22953754824474644 a^{4} + \frac{127971276283969603}{2} a^{3} + \frac{82841248537772215}{2} a^{2} - 124437453997146160 a + \frac{58288650921969011}{2} \) |
\( \bigl[a\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 3 a - 4\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -19 a^{4} + 73 a^{3} - 50 a^{2} - 27 a + 34\) , \( -198 a^{4} + 689 a^{3} - 226 a^{2} - 470 a + 128\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-3a-4\right){x}^{2}+\left(-19a^{4}+73a^{3}-50a^{2}-27a+34\right){x}-198a^{4}+689a^{3}-226a^{2}-470a+128$ |
| 4.1-c1 |
4.1-c |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.073848650$ |
$3571.683608$ |
1.88156506 |
\( 1524327 a^{4} - \frac{84165471}{16} a^{3} + \frac{24533271}{16} a^{2} + \frac{31020265}{8} a - \frac{16824393}{16} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -4 a^{4} + 15 a^{3} - 11 a^{2} - 3 a + 3\) , \( -28 a^{4} + 97 a^{3} - 31 a^{2} - 67 a + 18\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-4a^{4}+15a^{3}-11a^{2}-3a+3\right){x}-28a^{4}+97a^{3}-31a^{2}-67a+18$ |
| 4.1-c2 |
4.1-c |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$35.97335$ |
$(a^4-2a^3-3a^2+2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.036924325$ |
$7143.367217$ |
1.88156506 |
\( \frac{820447}{4} a^{4} - \frac{709589}{2} a^{3} - \frac{3669507}{4} a^{2} + \frac{2306179}{4} a + \frac{3089195}{4} \) |
\( \bigl[-a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( -a^{4} + a^{3} + 6 a^{2} - 2 a - 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} - 3 a + 5\) , \( -3 a^{4} + 9 a^{3} + 5 a^{2} - 20 a + 3\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-2a-4\right){x}^{2}+\left(a^{4}-a^{3}-5a^{2}-3a+5\right){x}-3a^{4}+9a^{3}+5a^{2}-20a+3$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$38.55528$ |
$(a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1.536676462$ |
$41.22561375$ |
2.03360114 |
\( -\frac{833130001850227671}{512} a^{4} + \frac{688867329077049611}{512} a^{3} + \frac{4140670582054670941}{512} a^{2} + \frac{381285000979757941}{128} a - \frac{88770029777421287}{64} \) |
\( \bigl[a^{2} - 2 a\) , \( a^{4} - 3 a^{3} - a^{2} + 6 a - 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -43 a^{4} + 158 a^{3} - 66 a^{2} - 121 a + 24\) , \( -576 a^{4} + 2020 a^{3} - 657 a^{2} - 1513 a + 417\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+6a-2\right){x}^{2}+\left(-43a^{4}+158a^{3}-66a^{2}-121a+24\right){x}-576a^{4}+2020a^{3}-657a^{2}-1513a+417$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{54} \) |
$38.55528$ |
$(a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$0.768338231$ |
$41.22561375$ |
2.03360114 |
\( -\frac{1912785483907}{131072} a^{4} + \frac{3150395092021}{262144} a^{3} + \frac{19023423484995}{262144} a^{2} + \frac{7075586246471}{262144} a - \frac{201023027837}{16384} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -65 a^{4} + 114 a^{3} + 282 a^{2} - 192 a - 231\) , \( -384 a^{4} + 657 a^{3} + 1707 a^{2} - 1067 a - 1436\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}^{2}+\left(-65a^{4}+114a^{3}+282a^{2}-192a-231\right){x}-384a^{4}+657a^{3}+1707a^{2}-1067a-1436$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$38.55528$ |
$(a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.256112743$ |
$10017.82414$ |
2.03360114 |
\( \frac{59223}{16} a^{4} - \frac{191559}{32} a^{3} - \frac{982835}{64} a^{2} + \frac{678135}{64} a + \frac{838055}{64} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -5 a^{4} + 9 a^{3} + 22 a^{2} - 17 a - 16\) , \( 6 a^{4} - 10 a^{3} - 28 a^{2} + 16 a + 24\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}^{2}+\left(-5a^{4}+9a^{3}+22a^{2}-17a-16\right){x}+6a^{4}-10a^{3}-28a^{2}+16a+24$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$38.55528$ |
$(a^4-2a^3-3a^2+3a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.512225487$ |
$10017.82414$ |
2.03360114 |
\( \frac{187161277}{4} a^{4} - \frac{647347259}{8} a^{3} - \frac{837220329}{4} a^{2} + \frac{262179971}{2} a + \frac{1412247867}{8} \) |
\( \bigl[a^{2} - 2 a\) , \( a^{4} - 3 a^{3} - a^{2} + 6 a - 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -3 a^{4} + 8 a^{3} + 4 a^{2} - 6 a - 6\) , \( 3 a^{4} - 7 a^{3} - 8 a^{2} + 8 a + 7\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+6a-2\right){x}^{2}+\left(-3a^{4}+8a^{3}+4a^{2}-6a-6\right){x}+3a^{4}-7a^{3}-8a^{2}+8a+7$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.109128526$ |
$1723.605548$ |
2.68355107 |
\( \frac{43659905638}{11} a^{4} - 6879578205 a^{3} - \frac{194822874707}{11} a^{2} + \frac{122678776584}{11} a + \frac{163699182145}{11} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a + 3\) , \( -a^{2} + 2 a - 2\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-3a-2\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(-a^{4}+2a^{3}+3a^{2}-5a+3\right){x}-a^{2}+2a-2$ |
| 11.1-b1 |
11.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{16} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$3.441754768$ |
$7.933945229$ |
3.11668419 |
\( -\frac{182358753622854757471478638399}{45949729863572161} a^{4} + \frac{13707443380590632114751520971}{4177248169415651} a^{3} + \frac{906325979355933512848040922053}{45949729863572161} a^{2} + \frac{333828555854135351628589722837}{45949729863572161} a - \frac{155442620771672002094158215846}{45949729863572161} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 6 a^{2} + 2 a + 5\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -35 a^{4} + 136 a^{3} - 74 a^{2} - 109 a + 45\) , \( -590 a^{4} + 2060 a^{3} - 654 a^{2} - 1533 a + 426\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+2a+5\right){x}^{2}+\left(-35a^{4}+136a^{3}-74a^{2}-109a+45\right){x}-590a^{4}+2060a^{3}-654a^{2}-1533a+426$ |
| 11.1-b2 |
11.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.430219346$ |
$16248.71982$ |
3.11668419 |
\( \frac{1096048}{121} a^{4} - \frac{193142}{11} a^{3} - \frac{4404245}{121} a^{2} + \frac{4806484}{121} a + \frac{5048146}{121} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} - a + 4\) , \( a + 1\) , \( a^{4} + a^{3} - 9 a^{2} - 8 a + 8\) , \( -6 a^{4} + 8 a^{3} + 24 a^{2} + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+4\right){x}^{2}+\left(a^{4}+a^{3}-9a^{2}-8a+8\right){x}-6a^{4}+8a^{3}+24a^{2}+1$ |
| 11.1-b3 |
11.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.860438692$ |
$8124.359914$ |
3.11668419 |
\( -\frac{796260890}{14641} a^{4} + \frac{201530448}{1331} a^{3} + \frac{1441935182}{14641} a^{2} - \frac{4306355025}{14641} a + \frac{1042905206}{14641} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 6 a^{2} + 2 a + 5\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( 6 a^{3} - 19 a^{2} + a + 15\) , \( -a^{4} + 8 a^{3} - 17 a^{2} + 2 a + 10\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+2a+5\right){x}^{2}+\left(6a^{3}-19a^{2}+a+15\right){x}-a^{4}+8a^{3}-17a^{2}+2a+10$ |
| 11.1-b4 |
11.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1.720877384$ |
$253.8862473$ |
3.11668419 |
\( \frac{15172281716252}{214358881} a^{4} - \frac{19303434235003}{19487171} a^{3} + \frac{274144431783988}{214358881} a^{2} + \frac{709743129570625}{214358881} a + \frac{279732592872002}{214358881} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 2\) , \( 1\) , \( 38 a^{4} - 108 a^{3} - 60 a^{2} + 205 a - 70\) , \( 59 a^{4} - 169 a^{3} - 91 a^{2} + 325 a - 112\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-2\right){x}^{2}+\left(38a^{4}-108a^{3}-60a^{2}+205a-70\right){x}+59a^{4}-169a^{3}-91a^{2}+325a-112$ |
| 11.1-b5 |
11.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.430219346$ |
$4062.179957$ |
3.11668419 |
\( -\frac{1773651723940}{121} a^{4} + \frac{449473822681}{11} a^{3} + \frac{3200600036578}{121} a^{2} - \frac{9615365125565}{121} a + \frac{2252001592100}{121} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -4 a^{3} + 5 a^{2} + 16 a + 2\) , \( 5 a^{4} - 5 a^{3} - 24 a^{2} - 6 a + 4\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+2\right){x}^{2}+\left(-4a^{3}+5a^{2}+16a+2\right){x}+5a^{4}-5a^{3}-24a^{2}-6a+4$ |
| 11.1-b6 |
11.1-b |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$3.441754768$ |
$7.933945229$ |
3.11668419 |
\( \frac{27797622415386831}{14641} a^{4} - \frac{4973366170167195}{1331} a^{3} - \frac{77206498196591605}{14641} a^{2} + \frac{67049494314574843}{14641} a + \frac{63276245675572246}{14641} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 6 a^{2} + 2 a + 5\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a + 1\) , \( -775 a^{4} + 2666 a^{3} - 774 a^{2} - 1959 a + 525\) , \( -29490 a^{4} + 101682 a^{3} - 29506 a^{2} - 74975 a + 20248\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+2a+5\right){x}^{2}+\left(-775a^{4}+2666a^{3}-774a^{2}-1959a+525\right){x}-29490a^{4}+101682a^{3}-29506a^{2}-74975a+20248$ |
| 11.1-c1 |
11.1-c |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.084326717$ |
$5662.560466$ |
3.40629096 |
\( \frac{73484050116}{121} a^{4} - \frac{23054690826}{11} a^{3} + \frac{73963504643}{121} a^{2} + \frac{186935159527}{121} a - \frac{50819826220}{121} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{2} - a - 1\) , \( -2 a^{4} + 9 a^{3} - 7 a^{2} - 11 a + 2\) , \( 13 a^{4} - 31 a^{3} - 19 a^{2} + 10 a - 1\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-2a^{4}+9a^{3}-7a^{2}-11a+2\right){x}+13a^{4}-31a^{3}-19a^{2}+10a-1$ |
| 11.1-c2 |
11.1-c |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.168653435$ |
$5662.560466$ |
3.40629096 |
\( \frac{3594658389050}{11} a^{4} - 566417217733 a^{3} - \frac{16040389054658}{11} a^{2} + \frac{10100526104492}{11} a + \frac{13477880002374}{11} \) |
\( \bigl[a\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a - 1\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a\) , \( -3 a^{4} + 6 a^{3} + 9 a^{2} - 10 a\) , \( 2 a^{4} - 5 a^{3} - 4 a^{2} + 9 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+8a-1\right){x}^{2}+\left(-3a^{4}+6a^{3}+9a^{2}-10a\right){x}+2a^{4}-5a^{3}-4a^{2}+9a-2$ |
| 11.1-d1 |
11.1-d |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{18} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.007842804$ |
$16.76645971$ |
2.16131109 |
\( -\frac{4753815926957848319736451833163}{5559917313492231481} a^{4} + \frac{749068196401608884275317432507}{505447028499293771} a^{3} + \frac{21212872652106169992983750877698}{5559917313492231481} a^{2} - \frac{13357616622639770128088399343510}{5559917313492231481} a - \frac{17824033662484010697962078348743}{5559917313492231481} \) |
\( \bigl[a\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( -20 a^{4} + 42 a^{3} + 75 a^{2} - 76 a - 72\) , \( -85 a^{4} + 160 a^{3} + 361 a^{2} - 276 a - 346\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a+1\right){x}^{2}+\left(-20a^{4}+42a^{3}+75a^{2}-76a-72\right){x}-85a^{4}+160a^{3}+361a^{2}-276a-346$ |
| 11.1-d2 |
11.1-d |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{6} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.669280934$ |
$4074.249711$ |
2.16131109 |
\( -\frac{117918850139}{1771561} a^{4} - \frac{56774289791}{161051} a^{3} + \frac{1967304724019}{1771561} a^{2} + \frac{1258523369089}{1771561} a - \frac{488887577751}{1771561} \) |
\( \bigl[a\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( -a^{3} + 2 a^{2} + 2 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a+1\right){x}^{2}+\left(2a^{3}-5a^{2}-6a+3\right){x}-a^{3}+2a^{2}+2a-2$ |
| 11.1-d3 |
11.1-d |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.338561869$ |
$4074.249711$ |
2.16131109 |
\( \frac{41531180214063}{1331} a^{4} + \frac{2995819798977}{121} a^{3} - \frac{73591906332212}{1331} a^{2} - \frac{38944579756372}{1331} a + \frac{15096149382991}{1331} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a\) , \( 33 a^{4} - 84 a^{3} - 75 a^{2} + 150 a - 27\) , \( -136 a^{4} + 336 a^{3} + 316 a^{2} - 576 a + 127\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4\right){x}^{2}+\left(33a^{4}-84a^{3}-75a^{2}+150a-27\right){x}-136a^{4}+336a^{3}+316a^{2}-576a+127$ |
| 11.1-d4 |
11.1-d |
$4$ |
$6$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{9} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$4.015685608$ |
$16.76645971$ |
2.16131109 |
\( \frac{7159884384958833117692883418998441}{2357947691} a^{4} - \frac{1128197172437232180197297521454230}{214358881} a^{3} - \frac{31949431342084769731820122553212350}{2357947691} a^{2} + \frac{20118362230791258979448925303524798}{2357947691} a + \frac{26845385322810509473726358706335601}{2357947691} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a\) , \( 138 a^{4} - 459 a^{3} - 130 a^{2} + 1020 a - 252\) , \( 2379 a^{4} - 5799 a^{3} - 5636 a^{2} + 9821 a - 2126\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4\right){x}^{2}+\left(138a^{4}-459a^{3}-130a^{2}+1020a-252\right){x}+2379a^{4}-5799a^{3}-5636a^{2}+9821a-2126$ |
| 11.1-e1 |
11.1-e |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$39.80285$ |
$(-a^2+a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$215.6545146$ |
1.85003002 |
\( -\frac{693188919441787}{11} a^{4} + 52105249397718 a^{3} + \frac{3445160187912835}{11} a^{2} + \frac{1268961495374690}{11} a - \frac{590874276860576}{11} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 1\) , \( 2 a^{4} - 8 a^{3} + 5 a^{2} + 3 a - 2\) , \( -2 a^{4} + 6 a^{3} - a^{2} - 5 a + 1\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(2a^{4}-8a^{3}+5a^{2}+3a-2\right){x}-2a^{4}+6a^{3}-a^{2}-5a+1$ |
| 11.1-e2 |
11.1-e |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$215.6545146$ |
1.85003002 |
\( \frac{3497685064340196359480}{214358881} a^{4} - \frac{1097095408990006956697}{19487171} a^{3} + \frac{3511506132297795269930}{214358881} a^{2} + \frac{8898016192405336244276}{214358881} a - \frac{2411703907841084733270}{214358881} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -6 a^{4} + 11 a^{3} + 19 a^{2} - 9 a - 10\) , \( -a^{4} + 6 a^{3} - 14 a^{2} + 3 a + 14\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-6a^{4}+11a^{3}+19a^{2}-9a-10\right){x}-a^{4}+6a^{3}-14a^{2}+3a+14$ |
| 11.1-e3 |
11.1-e |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$1725.236117$ |
1.85003002 |
\( \frac{16546118812}{14641} a^{4} - \frac{5190316424}{1331} a^{3} + \frac{16801855685}{14641} a^{2} + \frac{41884212039}{14641} a - \frac{11338793030}{14641} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -a^{4} + a^{3} + 4 a^{2} + a\) , \( -a^{4} + a^{3} + 3 a^{2} - a - 2\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}+a\right){x}-a^{4}+a^{3}+3a^{2}-a-2$ |
| 11.1-e4 |
11.1-e |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$862.6180587$ |
1.85003002 |
\( \frac{6456304270}{121} a^{4} + \frac{514373289}{11} a^{3} - \frac{10356512444}{121} a^{2} - \frac{5697888078}{121} a + \frac{2216950504}{121} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{3} - 3 a^{2} + 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( 14 a^{4} - 22 a^{3} - 51 a^{2} + 8 a - 2\) , \( 19 a^{4} + a^{3} - 118 a^{2} - 101 a + 17\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-3a^{2}+2\right){x}^{2}+\left(14a^{4}-22a^{3}-51a^{2}+8a-2\right){x}+19a^{4}+a^{3}-118a^{2}-101a+17$ |
| 11.1-e5 |
11.1-e |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$39.80285$ |
$(-a^2+a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$862.6180587$ |
1.85003002 |
\( -\frac{13565547829}{121} a^{4} + \frac{3437714554}{11} a^{3} + \frac{24479781879}{121} a^{2} - \frac{73540500074}{121} a + \frac{17223941626}{121} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} - a + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a - 1\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a\) , \( a^{4} - 7 a^{2} - 2 a + 5\) , \( 2 a^{4} - 5 a^{3} - 5 a^{2} + 9 a - 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}-a+3\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a-1\right){x}^{2}+\left(a^{4}-7a^{2}-2a+5\right){x}+2a^{4}-5a^{3}-5a^{2}+9a-2$ |
| 11.1-e6 |
11.1-e |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$39.80285$ |
$(-a^2+a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$53.91362867$ |
1.85003002 |
\( \frac{2164534405417343871}{11} a^{4} + 157030484138130886 a^{3} - \frac{3825012249883084179}{11} a^{2} - \frac{2044299341624061078}{11} a + \frac{773601471507805880}{11} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{3} - 3 a^{2} + 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( -36 a^{4} + 83 a^{3} + 124 a^{2} - 177 a - 97\) , \( -194 a^{4} + 409 a^{3} + 739 a^{2} - 804 a - 618\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+2a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-3a^{2}+2\right){x}^{2}+\left(-36a^{4}+83a^{3}+124a^{2}-177a-97\right){x}-194a^{4}+409a^{3}+739a^{2}-804a-618$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$41.32253$ |
$(a^4-2a^3-3a^2+2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.053515425$ |
$16349.80314$ |
3.12079479 |
\( 1528339393814 a^{4} - 5273223572639 a^{3} + 1534378505080 a^{2} + 3888054073542 a - 1053811794727 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 1\) , \( -40 a^{4} + 141 a^{3} - 48 a^{2} - 102 a + 31\) , \( 335 a^{4} - 1155 a^{3} + 335 a^{2} + 850 a - 229\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a+1\right){x}^{2}+\left(-40a^{4}+141a^{3}-48a^{2}-102a+31\right){x}+335a^{4}-1155a^{3}+335a^{2}+850a-229$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$41.32253$ |
$(a^4-2a^3-3a^2+2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.107030851$ |
$8174.901571$ |
3.12079479 |
\( -2612476 a^{4} + 3073678 a^{3} + 10905701 a^{2} + 3252983 a - 1688453 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{4} + 3 a^{3} + a^{2} - 4 a\) , \( a^{2} - a - 1\) , \( a^{4} - 3 a^{3} + 2 a\) , \( 3 a^{4} - 5 a^{3} - 12 a^{2} + 11 a + 6\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-4a\right){x}^{2}+\left(a^{4}-3a^{3}+2a\right){x}+3a^{4}-5a^{3}-12a^{2}+11a+6$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$41.32253$ |
$(a^4-2a^3-3a^2+2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.063116047$ |
$3513.636217$ |
2.37296613 |
\( -297939 a^{4} + 771727 a^{3} + 632626 a^{2} - 1398165 a + 315529 \) |
\( \bigl[a^{3} - a^{2} - 5 a + 2\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 6 a + 1\) , \( 0\) , \( 2 a^{4} - 6 a^{3} - 4 a^{2} + 11 a + 9\) , \( 5 a^{4} - 10 a^{3} - 18 a^{2} + 17 a + 18\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+2\right){x}{y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+6a+1\right){x}^{2}+\left(2a^{4}-6a^{3}-4a^{2}+11a+9\right){x}+5a^{4}-10a^{3}-18a^{2}+17a+18$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$41.32253$ |
$(a^4-2a^3-3a^2+2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.031558023$ |
$7027.272434$ |
2.37296613 |
\( -352955918543 a^{4} + 983896098031 a^{3} + 636917774568 a^{2} - 1913453221799 a + 448147259151 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{4} + 3 a^{3} + a^{2} - 4 a + 1\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a + 1\) , \( -a^{4} + 5 a^{3} - a^{2} - 10 a - 3\) , \( 12 a^{4} - 16 a^{3} - 48 a^{2} - 3 a + 7\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-4a+1\right){x}^{2}+\left(-a^{4}+5a^{3}-a^{2}-10a-3\right){x}+12a^{4}-16a^{3}-48a^{2}-3a+7$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$41.57380$ |
$(a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.023618075$ |
$9144.180231$ |
3.08122190 |
\( -\frac{699572}{17} a^{4} + \frac{1219241}{17} a^{3} + \frac{3104929}{17} a^{2} - \frac{1982533}{17} a - \frac{2590782}{17} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 2\) , \( a^{2} - a - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{4} - 4 a^{3} + a^{2} + 7 a\) , \( 2 a^{4} - 6 a^{3} - 2 a^{2} + 9 a - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+2\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(a^{4}-4a^{3}+a^{2}+7a\right){x}+2a^{4}-6a^{3}-2a^{2}+9a-3$ |
| 17.1-b1 |
17.1-b |
$4$ |
$4$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{4} \) |
$41.57380$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.047208862$ |
$5086.861246$ |
1.71307795 |
\( -\frac{8606045075}{83521} a^{4} + \frac{6973704336}{83521} a^{3} + \frac{42582910815}{83521} a^{2} + \frac{15680673636}{83521} a - \frac{7332731786}{83521} \) |
\( \bigl[-a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( -a^{2} + 2 a\) , \( a^{2} - 2 a - 1\) , \( 3 a^{3} - 7 a^{2} - 5 a + 1\) , \( 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{2}+2a\right){x}^{2}+\left(3a^{3}-7a^{2}-5a+1\right){x}+2a^{4}-9a^{3}+7a^{2}+8a-3$ |
| 17.1-b2 |
17.1-b |
$4$ |
$4$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$41.57380$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.094417725$ |
$10173.72249$ |
1.71307795 |
\( \frac{15691453948}{289} a^{4} + \frac{12327454328}{289} a^{3} - \frac{27874466151}{289} a^{2} - \frac{14556132621}{289} a + \frac{5813922518}{289} \) |
\( \bigl[1\) , \( -2 a^{4} + 5 a^{3} + 5 a^{2} - 9 a\) , \( a^{2} - a\) , \( -4 a^{4} + 11 a^{3} + 4 a^{2} - 18 a + 5\) , \( -a^{4} + 3 a^{3} + 4 a^{2} - 9 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-2a^{4}+5a^{3}+5a^{2}-9a\right){x}^{2}+\left(-4a^{4}+11a^{3}+4a^{2}-18a+5\right){x}-a^{4}+3a^{3}+4a^{2}-9a+2$ |
| 17.1-b3 |
17.1-b |
$4$ |
$4$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$41.57380$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.188835450$ |
$2543.430623$ |
1.71307795 |
\( \frac{3361930609274}{17} a^{4} - \frac{5826902017155}{17} a^{3} - \frac{15002654791610}{17} a^{2} + \frac{9445842219164}{17} a + \frac{12606728911324}{17} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( 2 a^{4} - 4 a^{3} - 7 a^{2} + 6 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 3\) , \( 5 a^{4} - 19 a^{3} - 15 a^{2} + 33 a\) , \( 2 a^{4} + 26 a^{3} - 5 a^{2} - 47 a + 13\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3\right){y}={x}^{3}+\left(2a^{4}-4a^{3}-7a^{2}+6a+4\right){x}^{2}+\left(5a^{4}-19a^{3}-15a^{2}+33a\right){x}+2a^{4}+26a^{3}-5a^{2}-47a+13$ |
| 17.1-b4 |
17.1-b |
$4$ |
$4$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$41.57380$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.188835450$ |
$2543.430623$ |
1.71307795 |
\( \frac{3111511323809746538}{17} a^{4} + \frac{2483044854063098009}{17} a^{3} - \frac{5498435322582483784}{17} a^{2} - \frac{2938682980363918540}{17} a + \frac{1112040540352113770}{17} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( -22 a^{4} + 38 a^{3} + 95 a^{2} - 49 a - 93\) , \( -37 a^{4} + 50 a^{3} + 205 a^{2} - 88 a - 191\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+3a+1\right){x}^{2}+\left(-22a^{4}+38a^{3}+95a^{2}-49a-93\right){x}-37a^{4}+50a^{3}+205a^{2}-88a-191$ |
| 17.2-a1 |
17.2-a |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$41.57380$ |
$(-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.446928341$ |
$434.8033486$ |
2.77245475 |
\( \frac{861725508378016}{17} a^{4} - \frac{2973332906398430}{17} a^{3} + \frac{865399101049481}{17} a^{2} + \frac{2192445141000476}{17} a - \frac{594211472536253}{17} \) |
\( \bigl[-a^{4} + 3 a^{3} + 2 a^{2} - 6 a\) , \( -a^{4} + a^{3} + 6 a^{2} - a - 4\) , \( a^{2} - 2 a\) , \( -16 a^{4} + 49 a^{3} + a^{2} - 30 a - 14\) , \( 57 a^{4} - 208 a^{3} + 98 a^{2} + 127 a - 58\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+2a^{2}-6a\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-a-4\right){x}^{2}+\left(-16a^{4}+49a^{3}+a^{2}-30a-14\right){x}+57a^{4}-208a^{3}+98a^{2}+127a-58$ |
| 17.2-a2 |
17.2-a |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$41.57380$ |
$(-a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.223464170$ |
$6956.853577$ |
2.77245475 |
\( \frac{297482089}{289} a^{4} - \frac{1220133564}{289} a^{3} + \frac{1095567866}{289} a^{2} - \frac{15837720}{289} a - \frac{37652731}{289} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 3 a + 6\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a + 1\) , \( 21 a^{4} - 23 a^{3} - 97 a^{2} - 16 a + 21\) , \( 57 a^{4} - 49 a^{3} - 279 a^{2} - 99 a + 41\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(-a^{4}+3a^{3}+2a^{2}-7a+1\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-9a^{2}+3a+6\right){x}^{2}+\left(21a^{4}-23a^{3}-97a^{2}-16a+21\right){x}+57a^{4}-49a^{3}-279a^{2}-99a+41$ |
| 17.2-a3 |
17.2-a |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{2} \) |
$41.57380$ |
$(-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.055866042$ |
$6956.853577$ |
2.77245475 |
\( -\frac{22556967}{289} a^{4} + \frac{21983781}{289} a^{3} + \frac{106661441}{289} a^{2} + \frac{29030281}{289} a - \frac{15275885}{289} \) |
\( \bigl[a^{2} - a\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a - 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 2 a + 3\) , \( 2 a^{4} + a^{3} - 3 a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-8a-1\right){x}^{2}+\left(-a^{4}+2a^{3}+3a^{2}-2a+3\right){x}+2a^{4}+a^{3}-3a^{2}-2a-1$ |
| 17.2-a4 |
17.2-a |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.2 |
\( 17 \) |
\( 17^{4} \) |
$41.57380$ |
$(-a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.111732085$ |
$13913.70715$ |
2.77245475 |
\( \frac{62446343}{83521} a^{4} - \frac{18389813}{83521} a^{3} - \frac{67965818}{83521} a^{2} - \frac{54150044}{83521} a + \frac{218090633}{83521} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} - a + 4\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( -4 a^{4} + 8 a^{3} + 10 a^{2} - a - 2\) , \( 2 a^{4} - 10 a^{3} + 9 a^{2} + 8 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}-a+4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-4a^{4}+8a^{3}+10a^{2}-a-2\right){x}+2a^{4}-10a^{3}+9a^{2}+8a-3$ |
| 17.2-a5 |
17.2-a |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.2 |
\( 17 \) |
\( 17^{8} \) |
$41.57380$ |
$(-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.223464170$ |
$1739.213394$ |
2.77245475 |
\( \frac{137660954362296989}{6975757441} a^{4} + \frac{100340217139406526}{6975757441} a^{3} - \frac{253353662002809670}{6975757441} a^{2} - \frac{115914951522049710}{6975757441} a + \frac{61920231356665971}{6975757441} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} - a + 4\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( -14 a^{4} + 38 a^{3} + 15 a^{2} - 31 a - 2\) , \( -27 a^{4} + 91 a^{3} - 24 a^{2} - 63 a + 20\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}-a+4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-14a^{4}+38a^{3}+15a^{2}-31a-2\right){x}-27a^{4}+91a^{3}-24a^{2}-63a+20$ |
| 17.2-a6 |
17.2-a |
$6$ |
$8$ |
5.5.122821.1 |
$5$ |
$[5, 0]$ |
17.2 |
\( 17 \) |
\( -17 \) |
$41.57380$ |
$(-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.446928341$ |
$1739.213394$ |
2.77245475 |
\( -\frac{77174860507948}{17} a^{4} + \frac{215131808160238}{17} a^{3} + \frac{139263964639067}{17} a^{2} - \frac{418382237284456}{17} a + \frac{97988730206921}{17} \) |
\( \bigl[a^{2} - 2 a\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 2 a - 5\) , \( a^{4} - a^{3} - 5 a^{2} - a + 4\) , \( -a^{4} + 4 a^{3} - 6 a^{2} + 6 a + 8\) , \( -25 a^{4} + 38 a^{3} + 127 a^{2} - 67 a - 105\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}-a+4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-2a-5\right){x}^{2}+\left(-a^{4}+4a^{3}-6a^{2}+6a+8\right){x}-25a^{4}+38a^{3}+127a^{2}-67a-105$ |
*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.
