| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$44.63825$ |
$(a^4-5a^2+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1448.056347$ |
3.61111309 |
\( -\frac{32217243917}{3} a^{4} + 18007168092 a^{3} + \frac{124525089365}{3} a^{2} - \frac{213146129860}{3} a + \frac{47603120438}{3} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 5 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( -a^{4} + 5 a^{2} + a\) , \( 4 a^{4} + a^{3} - 19 a^{2} - 8 a + 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-5a-3\right){x}^{2}+\left(-a^{4}+5a^{2}+a\right){x}+4a^{4}+a^{3}-19a^{2}-8a+3$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$44.63825$ |
$(a^4-5a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.018468321$ |
$10888.10546$ |
2.50729464 |
\( \frac{747793342}{3} a^{4} - 753884124 a^{3} + \frac{839874611}{3} a^{2} + \frac{1290423893}{3} a - \frac{369335632}{3} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 3 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( -6 a^{4} + a^{3} + 26 a^{2} - 6 a - 11\) , \( -3 a^{4} - 4 a^{3} + 7 a^{2} + 6 a + 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+9a^{2}-3a-2\right){x}^{2}+\left(-6a^{4}+a^{3}+26a^{2}-6a-11\right){x}-3a^{4}-4a^{3}+7a^{2}+6a+1$ |
| 9.1-c1 |
9.1-c |
$4$ |
$15$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$44.63825$ |
$(a^4-5a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 1 \) |
$5.024095054$ |
$1.191540139$ |
1.86608819 |
\( -\frac{1362859584417210265552}{243} a^{4} - \frac{182839759416657436177}{27} a^{3} + \frac{3182056032798762423940}{243} a^{2} + \frac{1572554890893820547857}{243} a - \frac{617417963367380388536}{243} \) |
\( \bigl[a^{4} - 5 a^{2} + 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( 546 a^{4} - 878 a^{3} - 2142 a^{2} + 3424 a - 759\) , \( 13177 a^{4} - 21774 a^{3} - 51256 a^{2} + 85685 a - 18507\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(546a^{4}-878a^{3}-2142a^{2}+3424a-759\right){x}+13177a^{4}-21774a^{3}-51256a^{2}+85685a-18507$ |
| 9.1-c2 |
9.1-c |
$4$ |
$15$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$44.63825$ |
$(a^4-5a^2+3)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1.004819010$ |
$3723.562937$ |
1.86608819 |
\( -\frac{643713008378}{3} a^{4} + 156600161332 a^{3} + \frac{3345490169651}{3} a^{2} - \frac{1670996131882}{3} a - \frac{2382588076453}{3} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -a^{4} + 5 a^{2} - a - 3\) , \( a^{4} - 5 a^{2} + 2\) , \( 7 a^{4} - 9 a^{3} - 26 a^{2} + 38 a - 7\) , \( -13 a^{4} + 24 a^{3} + 51 a^{2} - 93 a + 20\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-a-3\right){x}^{2}+\left(7a^{4}-9a^{3}-26a^{2}+38a-7\right){x}-13a^{4}+24a^{3}+51a^{2}-93a+20$ |
| 9.1-c3 |
9.1-c |
$4$ |
$15$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$44.63825$ |
$(a^4-5a^2+3)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$0.334939670$ |
$11170.68881$ |
1.86608819 |
\( \frac{12379375}{27} a^{4} - \frac{37575164}{27} a^{3} + \frac{14317900}{27} a^{2} + \frac{21228419}{27} a - \frac{6342761}{27} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -a^{4} + 6 a^{2} - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -13 a^{4} + 8 a^{3} + 70 a^{2} - 28 a - 51\) , \( 54 a^{4} - 40 a^{3} - 279 a^{2} + 143 a + 197\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+5a\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-3\right){x}^{2}+\left(-13a^{4}+8a^{3}+70a^{2}-28a-51\right){x}+54a^{4}-40a^{3}-279a^{2}+143a+197$ |
| 9.1-c4 |
9.1-c |
$4$ |
$15$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{30} \) |
$44.63825$ |
$(a^4-5a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 1 \) |
$1.674698351$ |
$3.574620419$ |
1.86608819 |
\( -\frac{268605305861390829836407}{14348907} a^{4} + \frac{450394293457823967148907}{14348907} a^{3} + \frac{1038204841696182050112038}{14348907} a^{2} - \frac{1777066342417430001622352}{14348907} a + \frac{396882183492690134473523}{14348907} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( -a^{4} + 6 a^{2} - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -18 a^{4} - 42 a^{3} + 20 a^{2} + 67 a + 9\) , \( -3353 a^{4} + 1876 a^{3} + 16593 a^{2} - 7586 a - 11486\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+5a\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-3\right){x}^{2}+\left(-18a^{4}-42a^{3}+20a^{2}+67a+9\right){x}-3353a^{4}+1876a^{3}+16593a^{2}-7586a-11486$ |
| 9.2-a1 |
9.2-a |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$44.63825$ |
$(-a^2-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.213657328$ |
$3127.741073$ |
2.08311971 |
\( -\frac{1295644}{27} a^{4} + \frac{296218}{9} a^{3} + \frac{2240452}{9} a^{2} - 115543 a - \frac{4603277}{27} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{4} - 4 a^{2} + 1\) , \( -29 a^{4} + 22 a^{3} + 149 a^{2} - 81 a - 97\) , \( -92 a^{4} + 68 a^{3} + 476 a^{2} - 245 a - 333\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-29a^{4}+22a^{3}+149a^{2}-81a-97\right){x}-92a^{4}+68a^{3}+476a^{2}-245a-333$ |
| 9.2-a2 |
9.2-a |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{2} \) |
$44.63825$ |
$(-a^2-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.071219109$ |
$9383.223220$ |
2.08311971 |
\( \frac{229401032}{3} a^{4} + 92174417 a^{3} - 178281442 a^{2} - 88036422 a + \frac{103721755}{3} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 5 a + 4\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( 0\) , \( 7 a^{4} - 7 a^{3} - 35 a^{2} + 21 a + 30\) , \( 10 a^{4} - 7 a^{3} - 48 a^{2} + 24 a + 35\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+5a+4\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(7a^{4}-7a^{3}-35a^{2}+21a+30\right){x}+10a^{4}-7a^{3}-48a^{2}+24a+35$ |
| 9.2-a3 |
9.2-a |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$44.63825$ |
$(-a^2-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.427314656$ |
$781.9352683$ |
2.08311971 |
\( \frac{6141094616569}{729} a^{4} - \frac{1494126889099}{243} a^{3} - \frac{10638256868476}{243} a^{2} + \frac{1771228955758}{81} a + \frac{22729106038511}{729} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4 a + 5\) , \( -a^{3} + 4 a + 1\) , \( 0\) , \( -24 a^{4} + 12 a^{3} + 124 a^{2} - 36 a - 84\) , \( -220 a^{4} + 139 a^{3} + 1128 a^{2} - 468 a - 735\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+4a+5\right){x}{y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-24a^{4}+12a^{3}+124a^{2}-36a-84\right){x}-220a^{4}+139a^{3}+1128a^{2}-468a-735$ |
| 9.2-a4 |
9.2-a |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$44.63825$ |
$(-a^2-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.142438218$ |
$2345.805805$ |
2.08311971 |
\( \frac{1223907858623562754}{9} a^{4} + \frac{492579433599336253}{3} a^{3} - \frac{952529832892695578}{3} a^{2} - \frac{470730947491004851}{3} a + \frac{554458418858302370}{9} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 5 a + 4\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( 0\) , \( -8 a^{4} - 7 a^{3} + 30 a^{2} + 6 a - 15\) , \( -10 a^{4} + 64 a^{3} + 139 a^{2} - 137 a - 133\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+5a+4\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-8a^{4}-7a^{3}+30a^{2}+6a-15\right){x}-10a^{4}+64a^{3}+139a^{2}-137a-133$ |
| 9.3-a1 |
9.3-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$44.63825$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.011998716$ |
$10171.11186$ |
3.04339875 |
\( -10331 a^{4} - 1485 a^{3} + 14206 a^{2} + 5063 a - 1551 \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - 4 a^{2} + a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( 6 a^{4} - 8 a^{3} - 19 a^{2} + 39 a - 7\) , \( -59 a^{4} + 74 a^{3} + 246 a^{2} - 269 a + 52\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-4a^{2}+a+1\right){x}^{2}+\left(6a^{4}-8a^{3}-19a^{2}+39a-7\right){x}-59a^{4}+74a^{3}+246a^{2}-269a+52$ |
| 9.3-a2 |
9.3-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{3} \) |
$44.63825$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.035996150$ |
$3390.370622$ |
3.04339875 |
\( 461521 a^{4} + 103548 a^{3} - 2180923 a^{2} - 824570 a + 376333 \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{2} - 2\) , \( 3 a^{4} + 2 a^{3} - 11 a^{2} - 3 a + 7\) , \( 5 a^{4} - 15 a^{2} + 11 a - 1\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(3a^{4}+2a^{3}-11a^{2}-3a+7\right){x}+5a^{4}-15a^{2}+11a-1$ |
| 9.3-b1 |
9.3-b |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{3} \) |
$44.63825$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.026884599$ |
$4295.471666$ |
2.87985121 |
\( -10331 a^{4} - 1485 a^{3} + 14206 a^{2} + 5063 a - 1551 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 5 a + 3\) , \( a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{3} + 2 a^{2} + 8 a - 4\) , \( 3 a^{4} - 2 a^{3} - 12 a^{2} + 9 a - 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+5a+3\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-a^{3}+2a^{2}+8a-4\right){x}+3a^{4}-2a^{3}-12a^{2}+9a-2$ |
| 9.3-b2 |
9.3-b |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$44.63825$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.080653797$ |
$1431.823888$ |
2.87985121 |
\( 461521 a^{4} + 103548 a^{3} - 2180923 a^{2} - 824570 a + 376333 \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( a^{4} - 6 a^{2} + a + 5\) , \( a^{4} - 5 a^{2} + 3\) , \( 2 a^{4} + 5 a^{3} - 5 a^{2} - 13 a + 6\) , \( 7 a^{4} + 4 a^{3} - 26 a^{2} - 2 a + 16\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+3\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+5\right){x}^{2}+\left(2a^{4}+5a^{3}-5a^{2}-13a+6\right){x}+7a^{4}+4a^{3}-26a^{2}-2a+16$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$47.56942$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1806.587343$ |
2.25260267 |
\( -\frac{6305013282}{289} a^{4} + \frac{111511521455}{289} a^{3} + \frac{312426461031}{289} a^{2} + \frac{105425593932}{289} a - \frac{35862663406}{289} \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{4} - 5 a^{2} + 2\) , \( -2 a^{4} + 14 a^{3} + 4 a^{2} - 23 a - 4\) , \( 3 a^{4} + 23 a^{3} - 44 a^{2} - 3 a + 18\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-2a^{4}+14a^{3}+4a^{2}-23a-4\right){x}+3a^{4}+23a^{3}-44a^{2}-3a+18$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$47.56942$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3613.174686$ |
2.25260267 |
\( -\frac{45163}{17} a^{4} + \frac{122611}{17} a^{3} - \frac{20123}{17} a^{2} - \frac{866560}{17} a + \frac{113007}{17} \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{4} - 5 a^{2} + 2\) , \( 3 a^{4} + 4 a^{3} - 6 a^{2} - 8 a + 1\) , \( 6 a^{4} + 6 a^{3} - 18 a^{2} - a + 1\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(3a^{4}+4a^{3}-6a^{2}-8a+1\right){x}+6a^{4}+6a^{3}-18a^{2}-a+1$ |
| 23.1-a1 |
23.1-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23^{3} \) |
$49.02930$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.090143473$ |
$1635.437893$ |
1.83820513 |
\( -\frac{3661128950660}{12167} a^{4} + \frac{2672068842929}{12167} a^{3} + \frac{19027416255569}{12167} a^{2} - \frac{9503812691435}{12167} a - \frac{13550974320256}{12167} \) |
\( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{4} - 5 a^{2} + 3\) , \( -8 a^{4} + 8 a^{3} + 44 a^{2} - 24 a - 31\) , \( 18 a^{4} - 10 a^{3} - 90 a^{2} + 41 a + 62\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+{x}^{2}+\left(-8a^{4}+8a^{3}+44a^{2}-24a-31\right){x}+18a^{4}-10a^{3}-90a^{2}+41a+62$ |
| 23.1-a2 |
23.1-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$49.02930$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.030047824$ |
$4906.313679$ |
1.83820513 |
\( \frac{764004229}{23} a^{4} + \frac{170689086}{23} a^{3} - \frac{3610206158}{23} a^{2} - \frac{1360750205}{23} a + \frac{623711407}{23} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( a - 1\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -3 a^{4} + 2 a^{3} + 14 a^{2} - 10 a - 11\) , \( 6 a^{4} - 6 a^{3} - 33 a^{2} + 20 a + 25\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a^{4}+2a^{3}+14a^{2}-10a-11\right){x}+6a^{4}-6a^{3}-33a^{2}+20a+25$ |
| 27.1-a1 |
27.1-a |
$2$ |
$2$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{18} \) |
$49.82179$ |
$(-a^4+5a^2+a-3), (a^4-5a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.021777834$ |
$2307.090173$ |
4.38533656 |
\( -\frac{12282248}{2187} a^{4} - \frac{262708}{243} a^{3} + \frac{57820412}{2187} a^{2} + \frac{21681152}{2187} a - \frac{10423585}{2187} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 6 a^{2} + 5 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 4\) , \( 4 a^{4} - 3 a^{3} - 21 a^{2} + 13 a + 10\) , \( -2 a^{3} + 11 a^{2} - 16 a + 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+5a+3\right){x}^{2}+\left(4a^{4}-3a^{3}-21a^{2}+13a+10\right){x}-2a^{3}+11a^{2}-16a+3$ |
| 27.1-a2 |
27.1-a |
$2$ |
$2$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{30} \) |
$49.82179$ |
$(-a^4+5a^2+a-3), (a^4-5a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.043555668$ |
$1153.545086$ |
4.38533656 |
\( \frac{325929001558}{1594323} a^{4} - \frac{2016979137172}{4782969} a^{3} - \frac{1036209874274}{4782969} a^{2} + \frac{55007514818}{531441} a + \frac{2449553128369}{4782969} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -24 a^{4} - 9 a^{3} + 115 a^{2} + 58 a - 24\) , \( 2670 a^{4} + 599 a^{3} - 12619 a^{2} - 4772 a + 2184\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-24a^{4}-9a^{3}+115a^{2}+58a-24\right){x}+2670a^{4}+599a^{3}-12619a^{2}-4772a+2184$ |
| 27.2-a1 |
27.2-a |
$2$ |
$2$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{24} \) |
$49.82179$ |
$(-a^4+5a^2+a-3), (-a^2-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$467.3798407$ |
2.33107153 |
\( -\frac{477977414581}{59049} a^{4} + \frac{6672175121}{6561} a^{3} + \frac{80912812208}{2187} a^{2} + \frac{38976347867}{19683} a - \frac{189391289903}{59049} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - 6 a^{2} + a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( 22 a^{4} - 5 a^{3} - 99 a^{2} + 7 a + 7\) , \( 71 a^{4} - 12 a^{3} - 314 a^{2} - 21 a + 27\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+5a+2\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+3\right){x}^{2}+\left(22a^{4}-5a^{3}-99a^{2}+7a+7\right){x}+71a^{4}-12a^{3}-314a^{2}-21a+27$ |
| 27.2-a2 |
27.2-a |
$2$ |
$2$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{12} \) |
$49.82179$ |
$(-a^4+5a^2+a-3), (-a^2-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1869.519363$ |
2.33107153 |
\( \frac{1319684}{27} a^{4} - \frac{36610780}{243} a^{3} + \frac{14368499}{243} a^{2} + \frac{21926675}{243} a - \frac{6199423}{243} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a - 5\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}^{2}+\left(2a^{4}-a^{3}-10a^{2}+3a+3\right){x}+a^{4}-2a^{3}-4a^{2}+7a-5$ |
| 27.3-a1 |
27.3-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{9} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.598531799$ |
$191.5205749$ |
3.81735323 |
\( -427494989356 a^{4} - 516154546680 a^{3} + 998118614091 a^{2} + 493260227393 a - 193665003027 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 4 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 5\) , \( 81 a^{4} - 64 a^{3} - 432 a^{2} + 218 a + 325\) , \( -809 a^{4} + 579 a^{3} + 4183 a^{2} - 2082 a - 2961\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+5a+2\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4a+5\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+9a^{2}-4a-1\right){x}^{2}+\left(81a^{4}-64a^{3}-432a^{2}+218a+325\right){x}-809a^{4}+579a^{3}+4183a^{2}-2082a-2961$ |
| 27.3-a2 |
27.3-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{3} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.532843933$ |
$574.5617249$ |
3.81735323 |
\( 7703725691309 a^{4} + 1723828200002 a^{3} - 36409066989213 a^{2} - 13741258119495 a + 6295099381698 \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 5 a + 5\) , \( 6 a^{4} - 9 a^{3} - 12 a^{2} + 31 a - 18\) , \( 29 a^{4} - 39 a^{3} - 117 a^{2} + 189 a - 50\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+3\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+5a+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){x}^{2}+\left(6a^{4}-9a^{3}-12a^{2}+31a-18\right){x}+29a^{4}-39a^{3}-117a^{2}+189a-50$ |
| 27.3-b1 |
27.3-b |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{5} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.305584306$ |
$330.3624283$ |
3.77631821 |
\( -8787557 a^{4} + 6413162 a^{3} + 45669594 a^{2} - 22810928 a - 32523451 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 5 a + 4\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{4} - 5 a^{2} + a + 3\) , \( -3 a^{4} + 4 a^{3} + 11 a^{2} - 17 a + 7\) , \( -7 a^{4} + 7 a^{3} + 32 a^{2} - 28 a - 8\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+5a+4\right){x}{y}+\left(a^{4}-5a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-3a^{4}+4a^{3}+11a^{2}-17a+7\right){x}-7a^{4}+7a^{3}+32a^{2}-28a-8$ |
| 27.3-b2 |
27.3-b |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{3} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.101861435$ |
$2973.261855$ |
3.77631821 |
\( 3559 a^{4} - 5363 a^{3} - 13821 a^{2} + 21110 a - 4615 \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 4\) , \( -a^{4} + 3 a^{3} + 6 a^{2} - 11 a - 3\) , \( a^{4} + 3 a^{3} - 4 a^{2} - 11 a - 1\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a\right){x}^{2}+\left(-a^{4}+3a^{3}+6a^{2}-11a-3\right){x}+a^{4}+3a^{3}-4a^{2}-11a-1$ |
| 27.3-c1 |
27.3-c |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{3} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$65.63797322$ |
1.47317147 |
\( -427494989356 a^{4} - 516154546680 a^{3} + 998118614091 a^{2} + 493260227393 a - 193665003027 \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 5\) , \( 3 a^{4} - 7 a^{3} - 27 a^{2} + 24 a + 23\) , \( 4 a^{4} - 44 a^{3} - 92 a^{2} + 93 a + 90\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+3\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4a+5\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}+3a+3\right){x}^{2}+\left(3a^{4}-7a^{3}-27a^{2}+24a+23\right){x}+4a^{4}-44a^{3}-92a^{2}+93a+90$ |
| 27.3-c2 |
27.3-c |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{9} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$196.9139196$ |
1.47317147 |
\( 7703725691309 a^{4} + 1723828200002 a^{3} - 36409066989213 a^{2} - 13741258119495 a + 6295099381698 \) |
\( \bigl[a^{2} + a - 1\) , \( a^{4} - 4 a^{2} - 1\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 19 a^{4} - 30 a^{3} - 71 a^{2} + 120 a - 26\) , \( -88 a^{4} + 150 a^{3} + 340 a^{2} - 587 a + 131\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}-1\right){x}^{2}+\left(19a^{4}-30a^{3}-71a^{2}+120a-26\right){x}-88a^{4}+150a^{3}+340a^{2}-587a+131$ |
| 27.3-d1 |
27.3-d |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{3} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.023106198$ |
$12732.75089$ |
3.66839742 |
\( -64276 a^{4} - 78814 a^{3} + 143547 a^{2} + 78861 a - 22575 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 4 a + 5\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -27 a^{4} + 45 a^{3} + 102 a^{2} - 181 a + 52\) , \( -189 a^{4} + 319 a^{3} + 727 a^{2} - 1260 a + 290\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+5a\right){y}={x}^{3}+\left(2a^{4}-a^{3}-11a^{2}+4a+5\right){x}^{2}+\left(-27a^{4}+45a^{3}+102a^{2}-181a+52\right){x}-189a^{4}+319a^{3}+727a^{2}-1260a+290$ |
| 27.3-d2 |
27.3-d |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{9} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.069318596$ |
$4244.250297$ |
3.66839742 |
\( 199781 a^{4} - 165912 a^{3} - 1009767 a^{2} + 603539 a + 629286 \) |
\( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 3\) , \( 1\) , \( 3 a^{4} - 14 a^{2} - 2 a + 5\) , \( 8 a^{4} + 2 a^{3} - 37 a^{2} - 13 a + 7\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}+{y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3a+3\right){x}^{2}+\left(3a^{4}-14a^{2}-2a+5\right){x}+8a^{4}+2a^{3}-37a^{2}-13a+7$ |
| 27.3-e1 |
27.3-e |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{9} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.004826000$ |
$5871.358825$ |
5.29959788 |
\( -64276 a^{4} - 78814 a^{3} + 143547 a^{2} + 78861 a - 22575 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a\) , \( a^{2} + a - 1\) , \( -2 a^{4} + 2 a^{3} + 6 a^{2} - 5 a\) , \( -2 a^{3} + 3 a^{2} - a\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a\right){x}^{2}+\left(-2a^{4}+2a^{3}+6a^{2}-5a\right){x}-2a^{3}+3a^{2}-a$ |
| 27.3-e2 |
27.3-e |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{3} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.043434008$ |
$1957.119608$ |
5.29959788 |
\( 199781 a^{4} - 165912 a^{3} - 1009767 a^{2} + 603539 a + 629286 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( a^{4} - 6 a^{2} + a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( a^{4} - 4 a^{2} - a + 4\) , \( -2 a^{4} + 2 a^{3} + 10 a^{2} - 6 a - 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+5\right){x}^{2}+\left(a^{4}-4a^{2}-a+4\right){x}-2a^{4}+2a^{3}+10a^{2}-6a-6$ |
| 27.3-f1 |
27.3-f |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{11} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.350934561$ |
$795.3577831$ |
3.48028098 |
\( -8787557 a^{4} + 6413162 a^{3} + 45669594 a^{2} - 22810928 a - 32523451 \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -7 a^{4} + 10 a^{3} + 29 a^{2} - 43 a + 8\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a + 1\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-7a^{4}+10a^{3}+29a^{2}-43a+8\right){x}-a^{4}+a^{3}+5a^{2}-6a+1$ |
| 27.3-f2 |
27.3-f |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{9} \) |
$49.82179$ |
$(-a^4+5a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.116978187$ |
$2386.073349$ |
3.48028098 |
\( 3559 a^{4} - 5363 a^{3} - 13821 a^{2} + 21110 a - 4615 \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -a^{4} + 4 a^{2} + a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 4\) , \( -2 a^{4} + 4 a^{3} + 16 a^{2} - 5 a - 9\) , \( 34 a^{4} - 19 a^{3} - 167 a^{2} + 81 a + 117\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a+1\right){x}^{2}+\left(-2a^{4}+4a^{3}+16a^{2}-5a-9\right){x}+34a^{4}-19a^{3}-167a^{2}+81a+117$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$50.51485$ |
$(a^3-4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.095077154$ |
$2873.915675$ |
3.40702898 |
\( \frac{43885}{31} a^{4} - \frac{54900}{31} a^{3} - \frac{212590}{31} a^{2} + \frac{268133}{31} a - \frac{7573}{31} \) |
\( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 5 a + 3\) , \( 3 a^{4} + 2 a^{3} - 8 a^{2} + 2 a + 3\) , \( -4 a^{4} - 3 a^{3} + 12 a^{2} + a - 6\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+5a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(3a^{4}+2a^{3}-8a^{2}+2a+3\right){x}-4a^{4}-3a^{3}+12a^{2}+a-6$ |
| 39.1-a1 |
39.1-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{15} \cdot 13^{9} \) |
$51.68796$ |
$(-a^4+5a^2+a-3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$3.064835803$ |
$103.3579900$ |
3.94981631 |
\( -\frac{13235714576779463953735}{152162975284735311} a^{4} + \frac{3282436225582669567145}{152162975284735311} a^{3} + \frac{19782258592439181379633}{50720991761578437} a^{2} - \frac{22061658056576296356190}{152162975284735311} a - \frac{38311727579005712725115}{152162975284735311} \) |
\( \bigl[a^{4} - 4 a^{2}\) , \( -2 a^{4} + a^{3} + 11 a^{2} - 5 a - 5\) , \( a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( 3 a^{4} + 4 a^{3} - 13 a^{2} - 25 a + 10\) , \( 22 a^{4} + 54 a^{3} - 127 a^{2} - 260 a + 94\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+5a+2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+11a^{2}-5a-5\right){x}^{2}+\left(3a^{4}+4a^{3}-13a^{2}-25a+10\right){x}+22a^{4}+54a^{3}-127a^{2}-260a+94$ |
| 39.1-a2 |
39.1-a |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{5} \cdot 13^{3} \) |
$51.68796$ |
$(-a^4+5a^2+a-3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.021611934$ |
$310.0739701$ |
3.94981631 |
\( \frac{188689766595926}{533871} a^{4} + \frac{42327906242276}{533871} a^{3} - \frac{297323017795892}{177957} a^{2} - \frac{336682810991971}{533871} a + \frac{154230690802159}{533871} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -2 a^{4} + a^{3} + 11 a^{2} - 5 a - 5\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 5 a + 5\) , \( 12 a^{4} - 5 a^{3} - 53 a^{2} + 22 a + 36\) , \( 15 a^{4} - 2 a^{3} - 62 a^{2} + 21 a + 36\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+5a+5\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+11a^{2}-5a-5\right){x}^{2}+\left(12a^{4}-5a^{3}-53a^{2}+22a+36\right){x}+15a^{4}-2a^{3}-62a^{2}+21a+36$ |
| 39.1-b1 |
39.1-b |
$4$ |
$4$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13 \) |
$51.68796$ |
$(-a^4+5a^2+a-3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$2.638052341$ |
$52.56497328$ |
3.45808356 |
\( -\frac{486547598361380247953}{1053} a^{4} - \frac{108868847939287244969}{1053} a^{3} + \frac{766500600484349063978}{351} a^{2} + \frac{867846211722362577886}{1053} a - \frac{397577874126278379139}{1053} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -a^{3} + 4 a - 1\) , \( a^{4} - 5 a^{2} + 2\) , \( -32 a^{4} + 14 a^{3} + 168 a^{2} - 51 a - 144\) , \( 169 a^{4} - 219 a^{3} - 989 a^{2} + 646 a + 710\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(-32a^{4}+14a^{3}+168a^{2}-51a-144\right){x}+169a^{4}-219a^{3}-989a^{2}+646a+710$ |
| 39.1-b2 |
39.1-b |
$4$ |
$4$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{2} \cdot 13^{2} \) |
$51.68796$ |
$(-a^4+5a^2+a-3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.319026170$ |
$841.0395726$ |
3.45808356 |
\( -\frac{424176582656}{1521} a^{4} - \frac{99307222046}{1521} a^{3} + \frac{667076720660}{507} a^{2} + \frac{777251653105}{1521} a - \frac{326914549519}{1521} \) |
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + 4 a^{2} + 1\) , \( a\) , \( -20 a^{4} + 67 a^{3} - 63 a^{2} + 25 a + 2\) , \( -292 a^{4} + 953 a^{3} - 594 a^{2} - 234 a + 92\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+4a^{2}+1\right){x}^{2}+\left(-20a^{4}+67a^{3}-63a^{2}+25a+2\right){x}-292a^{4}+953a^{3}-594a^{2}-234a+92$ |
| 39.1-b3 |
39.1-b |
$4$ |
$4$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3 \cdot 13 \) |
$51.68796$ |
$(-a^4+5a^2+a-3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.659513085$ |
$1682.079145$ |
3.45808356 |
\( \frac{324676}{39} a^{4} + \frac{17008}{39} a^{3} - \frac{514119}{13} a^{2} - \frac{311882}{39} a + \frac{383651}{39} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( a^{4} - 6 a^{2} + 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 5 a + 4\) , \( -9 a^{4} + 6 a^{3} + 46 a^{2} - 24 a - 30\) , \( 4 a^{4} - 2 a^{3} - 23 a^{2} + 8 a + 18\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+5a+4\right){y}={x}^{3}+\left(a^{4}-6a^{2}+4\right){x}^{2}+\left(-9a^{4}+6a^{3}+46a^{2}-24a-30\right){x}+4a^{4}-2a^{3}-23a^{2}+8a+18$ |
| 39.1-b4 |
39.1-b |
$4$ |
$4$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3 \cdot 13^{4} \) |
$51.68796$ |
$(-a^4+5a^2+a-3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.638052341$ |
$210.2598931$ |
3.45808356 |
\( \frac{5738121051463509119}{85683} a^{4} - \frac{4184808120813701401}{85683} a^{3} - \frac{9939190209637007734}{28561} a^{2} + \frac{14889511546489004030}{85683} a + \frac{21233613098139959581}{85683} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4 a + 5\) , \( -a^{2} + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( -82 a^{4} + 96 a^{3} + 454 a^{2} - 377 a - 467\) , \( 1150 a^{4} - 554 a^{3} - 5803 a^{2} + 1674 a + 3235\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+4a+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+5a+2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-82a^{4}+96a^{3}+454a^{2}-377a-467\right){x}+1150a^{4}-554a^{3}-5803a^{2}+1674a+3235$ |
| 51.1-a1 |
51.1-a |
$1$ |
$1$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3 \cdot 17 \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.245196627$ |
$1864.514368$ |
5.70040691 |
\( -\frac{4401380}{51} a^{4} - \frac{961874}{51} a^{3} + \frac{6945970}{17} a^{2} + \frac{7747873}{51} a - \frac{3787684}{51} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( 6 a^{3} + 9 a^{2} - 11 a - 10\) , \( 10 a^{4} + 3 a^{3} - 37 a^{2} + 6 a + 20\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+5a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(6a^{3}+9a^{2}-11a-10\right){x}+10a^{4}+3a^{3}-37a^{2}+6a+20$ |
| 51.1-b1 |
51.1-b |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( - 3^{9} \cdot 17^{3} \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$0.039407209$ |
$399.8883079$ |
5.30522474 |
\( \frac{39114810005}{96702579} a^{4} + \frac{33027699026}{96702579} a^{3} - \frac{64248149099}{32234193} a^{2} - \frac{111450288331}{96702579} a + \frac{14954638546}{96702579} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 5 a + 4\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{3} - a^{2} + a + 7\) , \( 31 a^{4} - 51 a^{3} - 122 a^{2} + 201 a - 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+5a+4\right){x}^{2}+\left(-a^{3}-a^{2}+a+7\right){x}+31a^{4}-51a^{3}-122a^{2}+201a-42$ |
| 51.1-b2 |
51.1-b |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( - 3^{3} \cdot 17 \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.118221628$ |
$1199.664923$ |
5.30522474 |
\( \frac{2956372247636}{459} a^{4} + \frac{1137654713156}{459} a^{3} - \frac{4943228725139}{153} a^{2} - \frac{5787733716511}{459} a + \frac{2607972404065}{459} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 5 a + 5\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( -23 a^{4} - 54 a^{3} + 15 a^{2} + 79 a + 32\) , \( 541 a^{4} + 612 a^{3} - 1326 a^{2} - 546 a + 319\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}+5a+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4a+5\right){x}^{2}+\left(-23a^{4}-54a^{3}+15a^{2}+79a+32\right){x}+541a^{4}+612a^{3}-1326a^{2}-546a+319$ |
| 51.1-c1 |
51.1-c |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{3} \cdot 17^{2} \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.180347685$ |
$270.1421618$ |
3.67209375 |
\( -\frac{3863826763601890}{7803} a^{4} - \frac{423666820160035}{7803} a^{3} + \frac{6020442703916440}{2601} a^{2} + \frac{4943276359194392}{7803} a - \frac{2624956889939675}{7803} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -95 a^{4} + 75 a^{3} + 477 a^{2} - 244 a - 341\) , \( 282 a^{4} - 234 a^{3} - 1391 a^{2} + 726 a + 991\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+5a\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3a+3\right){x}^{2}+\left(-95a^{4}+75a^{3}+477a^{2}-244a-341\right){x}+282a^{4}-234a^{3}-1391a^{2}+726a+991$ |
| 51.1-c2 |
51.1-c |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{18} \cdot 17^{3} \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$3.270521528$ |
$180.0947745$ |
3.67209375 |
\( -\frac{1148406599397820693}{1903396862457} a^{4} - \frac{1319671074071705731}{1903396862457} a^{3} + \frac{924325790758708426}{634465620819} a^{2} + \frac{1189930420790835560}{1903396862457} a - \frac{614646578782040741}{1903396862457} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 5 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( a + 2\) , \( -a^{4} + 4 a^{3} - 2 a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-11a^{2}+5a+5\right){x}^{2}+\left(a+2\right){x}-a^{4}+4a^{3}-2a^{2}-4a$ |
| 51.1-c3 |
51.1-c |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{6} \cdot 17 \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.090173842$ |
$540.2843237$ |
3.67209375 |
\( \frac{2706353294}{12393} a^{4} + \frac{2140005107}{12393} a^{3} - \frac{4496298041}{4131} a^{2} - \frac{11608629274}{12393} a + \frac{4078834822}{12393} \) |
\( \bigl[a^{4} - 4 a^{2}\) , \( -a^{4} + a^{3} + 6 a^{2} - 4 a - 3\) , \( a^{4} - 4 a^{2} + a\) , \( 12 a^{4} - 18 a^{3} - 46 a^{2} + 71 a - 11\) , \( 43 a^{4} - 71 a^{3} - 164 a^{2} + 282 a - 65\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-4a-3\right){x}^{2}+\left(12a^{4}-18a^{3}-46a^{2}+71a-11\right){x}+43a^{4}-71a^{3}-164a^{2}+282a-65$ |
| 51.1-c4 |
51.1-c |
$4$ |
$6$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{9} \cdot 17^{6} \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$6.541043057$ |
$90.04738729$ |
3.67209375 |
\( \frac{3793726213580112804612788}{475099770627} a^{4} + \frac{4579542196690148555482631}{475099770627} a^{3} - \frac{2953022011439423401006697}{158366590209} a^{2} - \frac{4375457150651451777405835}{475099770627} a + \frac{1720284905583487035733222}{475099770627} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 5 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( -50 a^{4} + 55 a^{3} + 210 a^{2} - 129 a - 158\) , \( 93 a^{4} + 22 a^{3} - 748 a^{2} + 280 a + 519\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-11a^{2}+5a+5\right){x}^{2}+\left(-50a^{4}+55a^{3}+210a^{2}-129a-158\right){x}+93a^{4}+22a^{3}-748a^{2}+280a+519$ |
| 51.1-d1 |
51.1-d |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3 \cdot 17^{3} \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$12.49526161$ |
2.52398053 |
\( -\frac{33988600772945805884081021}{14739} a^{4} - \frac{7605476790287527623258479}{14739} a^{3} + \frac{53545227879200403314311780}{4913} a^{2} + \frac{60626007183267127011786148}{14739} a - \frac{27773785361932926813615793}{14739} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 3 a - 3\) , \( a^{2} - 2\) , \( 138 a^{4} - 239 a^{3} - 528 a^{2} + 917 a - 200\) , \( 1872 a^{4} - 3115 a^{3} - 7221 a^{2} + 12317 a - 2752\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+9a^{2}-3a-3\right){x}^{2}+\left(138a^{4}-239a^{3}-528a^{2}+917a-200\right){x}+1872a^{4}-3115a^{3}-7221a^{2}+12317a-2752$ |
| 51.1-d2 |
51.1-d |
$2$ |
$3$ |
5.5.160801.1 |
$5$ |
$[5, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{3} \cdot 17 \) |
$53.09333$ |
$(-a^4+5a^2+a-3), (a^2-a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3036.348571$ |
2.52398053 |
\( -\frac{22982517266}{459} a^{4} - \frac{25897389185}{459} a^{3} + \frac{19386172109}{153} a^{2} + \frac{27701086222}{459} a - \frac{11100052360}{459} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 5 a\) , \( a^{2} + a - 1\) , \( 2 a^{3} - 3 a^{2} - 16 a + 5\) , \( 5 a^{4} + 6 a^{3} - 18 a^{2} - 18 a + 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+5a+2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-5a\right){x}^{2}+\left(2a^{3}-3a^{2}-16a+5\right){x}+5a^{4}+6a^{3}-18a^{2}-18a+6$ |
*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.
