| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$2$ |
$5$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.08016$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$4.580149802$ |
1.015057853 |
\( -2339506049812505 a^{2} + 2339506049812505 a + 15482930554544522 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 5 a + 5\) , \( a^{3} - 6 a - 5\) , \( 852 a^{3} + 548 a^{2} - 7038 a - 9278\) , \( 28818 a^{3} + 18782 a^{2} - 238321 a - 315051\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+5\right){x}^{2}+\left(852a^{3}+548a^{2}-7038a-9278\right){x}+28818a^{3}+18782a^{2}-238321a-315051$ |
| 1.1-a2 |
1.1-a |
$2$ |
$5$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.08016$ |
$\textsf{none}$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2862.593626$ |
1.015057853 |
\( -1225 a^{2} + 1225 a + 7657 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 5 a + 5\) , \( a^{3} - 6 a - 5\) , \( 2 a^{3} - 2 a^{2} - 13 a - 3\) , \( -a^{2} + a + 6\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+5\right){x}^{2}+\left(2a^{3}-2a^{2}-13a-3\right){x}-a^{2}+a+6$ |
| 11.2-a1 |
11.2-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$13.60321$ |
$(-a^3+6a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$96.18557875$ |
1.705340328 |
\( \frac{53439337193996624}{214358881} a^{3} + \frac{34948814168481960}{214358881} a^{2} - \frac{442051437137498072}{214358881} a - \frac{584955989119787177}{214358881} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{2} - 5\) , \( -30 a^{3} + 103 a^{2} + 125 a - 487\) , \( -168 a^{3} + 601 a^{2} + 674 a - 2874\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(-30a^{3}+103a^{2}+125a-487\right){x}-168a^{3}+601a^{2}+674a-2874$ |
| 11.2-b1 |
11.2-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$13.60321$ |
$(-a^3+6a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.043622373$ |
$902.5690851$ |
2.792227723 |
\( \frac{97207194933}{121} a^{3} - \frac{400561176236}{121} a^{2} - \frac{122604910301}{121} a + \frac{1329287856378}{121} \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{3} + 8 a + 5\) , \( a^{3} - 6 a - 6\) , \( 12 a^{3} + 7 a^{2} - 99 a - 126\) , \( 72 a^{3} + 47 a^{2} - 597 a - 791\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{3}-6a-6\right){y}={x}^{3}+\left(-a^{3}+8a+5\right){x}^{2}+\left(12a^{3}+7a^{2}-99a-126\right){x}+72a^{3}+47a^{2}-597a-791$ |
| 11.2-c1 |
11.2-c |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$13.60321$ |
$(-a^3+6a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.050271146$ |
$384.8036971$ |
2.743778882 |
\( \frac{195271897}{14641} a^{3} - \frac{796322217}{14641} a^{2} - \frac{247977731}{14641} a + \frac{2609722251}{14641} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{3} + 8 a + 6\) , \( a^{3} - 6 a - 5\) , \( -2 a^{3} + a^{2} + 16 a + 12\) , \( -4 a^{2} + 7 a + 32\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(-a^{3}+8a+6\right){x}^{2}+\left(-2a^{3}+a^{2}+16a+12\right){x}-4a^{2}+7a+32$ |
| 11.2-d1 |
11.2-d |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{6} \) |
$13.60321$ |
$(-a^3+6a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.848760694$ |
$142.5873199$ |
2.860921903 |
\( \frac{24388973560}{1771561} a^{3} - \frac{90587873214}{1771561} a^{2} - \frac{94422084530}{1771561} a + \frac{435711728413}{1771561} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{3} + 8 a + 5\) , \( a^{2} - a - 6\) , \( -a^{3} - 5 a^{2} + 14 a + 35\) , \( -a^{3} - 3 a^{2} + 12 a + 22\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{3}+8a+5\right){x}^{2}+\left(-a^{3}-5a^{2}+14a+35\right){x}-a^{3}-3a^{2}+12a+22$ |
| 11.2-d2 |
11.2-d |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$13.60321$ |
$(-a^3+6a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$2.546282084$ |
$1.760337283$ |
2.860921903 |
\( \frac{28643793854842421}{121} a^{3} - \frac{104613010753237251}{121} a^{2} - \frac{113595777834350168}{121} a + \frac{502764966330364967}{121} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{3} + 8 a + 5\) , \( a^{2} - a - 6\) , \( 54 a^{3} - 220 a^{2} - 56 a + 665\) , \( 596 a^{3} - 2374 a^{2} - 828 a + 7576\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{3}+8a+5\right){x}^{2}+\left(54a^{3}-220a^{2}-56a+665\right){x}+596a^{3}-2374a^{2}-828a+7576$ |
| 11.3-a1 |
11.3-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.3 |
\( 11 \) |
\( 11^{8} \) |
$13.60321$ |
$(a^2-2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$96.18557875$ |
1.705340328 |
\( -\frac{53439337193996624}{214358881} a^{3} + \frac{195266825750471832}{214358881} a^{2} + \frac{211835797218544280}{214358881} a - \frac{938619274894806665}{214358881} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 6 a + 6\) , \( a^{2} - 6\) , \( 29 a^{3} + 14 a^{2} - 237 a - 288\) , \( 167 a^{3} + 99 a^{2} - 1368 a - 1772\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{3}-2a^{2}-6a+6\right){x}^{2}+\left(29a^{3}+14a^{2}-237a-288\right){x}+167a^{3}+99a^{2}-1368a-1772$ |
| 11.3-b1 |
11.3-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.3 |
\( 11 \) |
\( 11^{2} \) |
$13.60321$ |
$(a^2-2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.043622373$ |
$902.5690851$ |
2.792227723 |
\( -\frac{97207194933}{121} a^{3} - \frac{108939591437}{121} a^{2} + \frac{632105677974}{121} a + \frac{903328964774}{121} \) |
\( \bigl[a^{2} - a - 6\) , \( a^{3} - 8 a - 6\) , \( a^{3} - 6 a - 6\) , \( -16 a^{3} + 49 a^{2} + 72 a - 219\) , \( -50 a^{3} + 189 a^{2} + 191 a - 924\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{3}-6a-6\right){y}={x}^{3}+\left(a^{3}-8a-6\right){x}^{2}+\left(-16a^{3}+49a^{2}+72a-219\right){x}-50a^{3}+189a^{2}+191a-924$ |
| 11.3-c1 |
11.3-c |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.3 |
\( 11 \) |
\( 11^{4} \) |
$13.60321$ |
$(a^2-2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.050271146$ |
$384.8036971$ |
2.743778882 |
\( -\frac{195271897}{14641} a^{3} - \frac{210506526}{14641} a^{2} + \frac{1254806474}{14641} a + \frac{1760694200}{14641} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 5\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -3 a^{3} + 4 a^{2} + 14 a + 4\) , \( -4 a^{3} + 11 a^{2} + 11 a - 29\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-8a-5\right){x}^{2}+\left(-3a^{3}+4a^{2}+14a+4\right){x}-4a^{3}+11a^{2}+11a-29$ |
| 11.3-d1 |
11.3-d |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.3 |
\( 11 \) |
\( 11^{6} \) |
$13.60321$ |
$(a^2-2a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.848760694$ |
$142.5873199$ |
2.860921903 |
\( -\frac{24388973560}{1771561} a^{3} - \frac{17420952534}{1771561} a^{2} + \frac{202430910278}{1771561} a + \frac{275090744229}{1771561} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 6\) , \( a^{2} - a - 5\) , \( -3 a^{3} - 3 a^{2} + 24 a + 36\) , \( a^{3} - 10 a - 12\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{3}-8a-6\right){x}^{2}+\left(-3a^{3}-3a^{2}+24a+36\right){x}+a^{3}-10a-12$ |
| 11.3-d2 |
11.3-d |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
11.3 |
\( 11 \) |
\( 11^{2} \) |
$13.60321$ |
$(a^2-2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$2.546282084$ |
$1.760337283$ |
2.860921903 |
\( -\frac{28643793854842421}{121} a^{3} - \frac{18681629188709988}{121} a^{2} + \frac{236890417776297407}{121} a + \frac{313199971597619969}{121} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 6\) , \( a^{2} - a - 5\) , \( -58 a^{3} - 53 a^{2} + 359 a + 436\) , \( -641 a^{3} - 660 a^{2} + 4121 a + 5573\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{3}-8a-6\right){x}^{2}+\left(-58a^{3}-53a^{2}+359a+436\right){x}-641a^{3}-660a^{2}+4121a+5573$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.25550$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.006115786$ |
$2223.964918$ |
3.858347183 |
\( -\frac{6297835481}{4} a^{2} + \frac{6297835481}{4} a + \frac{27631544681}{4} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{2} - a - 6\) , \( -273 a^{3} + 984 a^{2} + 1094 a - 4719\) , \( 5413 a^{3} - 19757 a^{2} - 21474 a + 94946\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-273a^{3}+984a^{2}+1094a-4719\right){x}+5413a^{3}-19757a^{2}-21474a+94946$ |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$14.56504$ |
$(a^3-a^2-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$235.2753967$ |
2.085679722 |
\( -\frac{69350388631}{6859} a^{3} - \frac{45292282430}{6859} a^{2} + \frac{573308883769}{6859} a + \frac{758083339011}{6859} \) |
\( \bigl[a^{3} - 6 a - 6\) , \( a^{3} - 7 a - 5\) , \( a^{3} - 7 a - 6\) , \( 6 a^{3} - 3 a^{2} - 38 a + 2\) , \( -4 a^{3} + 41 a^{2} - 6 a - 207\bigr] \) |
${y}^2+\left(a^{3}-6a-6\right){x}{y}+\left(a^{3}-7a-6\right){y}={x}^{3}+\left(a^{3}-7a-5\right){x}^{2}+\left(6a^{3}-3a^{2}-38a+2\right){x}-4a^{3}+41a^{2}-6a-207$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$14.56504$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$235.2753967$ |
2.085679722 |
\( \frac{69350388631}{6859} a^{3} - \frac{253343448323}{6859} a^{2} - \frac{274673153016}{6859} a + \frac{1216749551719}{6859} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a\) , \( 2 a^{3} + 2 a^{2} - 7 a - 4\) , \( 22 a^{3} + 19 a^{2} - 160 a - 217\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(2a^{3}+2a^{2}-7a-4\right){x}+22a^{3}+19a^{2}-160a-217$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.093679123$ |
$1056.973095$ |
3.511056724 |
\( -\frac{353851952629}{5} a^{3} - \frac{396567556972}{5} a^{2} + \frac{2300983001628}{5} a + \frac{3288322692713}{5} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{3} - 6 a - 5\) , \( -52 a^{3} - 54 a^{2} + 335 a + 462\) , \( 508 a^{3} + 576 a^{2} - 3307 a - 4758\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-52a^{3}-54a^{2}+335a+462\right){x}+508a^{3}+576a^{2}-3307a-4758$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.303646756$ |
$295.4869095$ |
3.181544397 |
\( -\frac{73728}{5} a^{3} + 53248 a^{2} + \frac{294912}{5} a - \frac{1273856}{5} \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 6 a - 6\) , \( a + 1\) , \( -4 a^{2} + 4 a + 27\) , \( -a^{3} + a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a-6\right){x}^{2}+\left(-4a^{2}+4a+27\right){x}-a^{3}+a^{2}+6a-2$ |
| 25.1-c1 |
25.1-c |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$193.9579240$ |
1.719406766 |
\( \frac{40211406}{25} a^{3} - \frac{165420729}{25} a^{2} - \frac{10484108}{5} a + \frac{552437089}{25} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{2} - 7\) , \( a^{3} - a^{2} - 6 a\) , \( 4 a^{3} - 26 a - 21\) , \( -3 a^{3} + 27 a + 27\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(4a^{3}-26a-21\right){x}-3a^{3}+27a+27$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.111345368$ |
$432.4113281$ |
3.414525113 |
\( \frac{228261}{5} a^{3} + \frac{120579}{5} a^{2} - \frac{1846428}{5} a - \frac{2349299}{5} \) |
\( \bigl[1\) , \( a^{2} - a - 7\) , \( a^{3} - 7 a - 5\) , \( -2 a^{2} + 2 a + 13\) , \( 5 a^{2} - 4 a - 31\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-7a-5\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-2a^{2}+2a+13\right){x}+5a^{2}-4a-31$ |
| 25.1-e1 |
25.1-e |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$193.9579240$ |
1.719406766 |
\( -\frac{40211406}{25} a^{3} - \frac{44786511}{25} a^{2} + \frac{52525556}{5} a + \frac{374807226}{25} \) |
\( \bigl[a^{3} - 6 a - 5\) , \( -a^{3} + 2 a^{2} + 5 a - 6\) , \( a^{3} - 7 a - 5\) , \( a^{3} + 4 a^{2} - 8 a - 26\) , \( 9 a^{3} - 21 a^{2} - 43 a + 90\bigr] \) |
${y}^2+\left(a^{3}-6a-5\right){x}{y}+\left(a^{3}-7a-5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-6\right){x}^{2}+\left(a^{3}+4a^{2}-8a-26\right){x}+9a^{3}-21a^{2}-43a+90$ |
| 25.1-f1 |
25.1-f |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.111345368$ |
$432.4113281$ |
3.414525113 |
\( -\frac{228261}{5} a^{3} + \frac{805362}{5} a^{2} + \frac{920487}{5} a - \frac{3846887}{5} \) |
\( \bigl[1\) , \( a^{2} - a - 7\) , \( a^{3} - a^{2} - 6 a + 1\) , \( -a^{3} + 7 a + 7\) , \( 5 a^{2} - 7 a - 29\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-6a+1\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-a^{3}+7a+7\right){x}+5a^{2}-7a-29$ |
| 25.1-g1 |
25.1-g |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.093679123$ |
$1056.973095$ |
3.511056724 |
\( \frac{353851952629}{5} a^{3} - \frac{1458123414859}{5} a^{2} - \frac{446292029797}{5} a + 967777236948 \) |
\( \bigl[1\) , \( a\) , \( a^{3} - a^{2} - 5 a\) , \( 51 a^{3} - 208 a^{2} - 67 a + 686\) , \( -509 a^{3} + 2102 a^{2} + 634 a - 6985\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+a{x}^{2}+\left(51a^{3}-208a^{2}-67a+686\right){x}-509a^{3}+2102a^{2}+634a-6985$ |
| 25.1-h1 |
25.1-h |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$15.07336$ |
$(2a^2-2a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.303646756$ |
$295.4869095$ |
3.181544397 |
\( \frac{73728}{5} a^{3} + \frac{45056}{5} a^{2} - \frac{606208}{5} a - \frac{786432}{5} \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 7 a + 1\) , \( a\) , \( -4 a^{2} + 4 a + 27\) , \( a^{3} - 2 a^{2} - 6 a + 5\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{3}-a^{2}-7a+1\right){x}^{2}+\left(-4a^{2}+4a+27\right){x}+a^{3}-2a^{2}-6a+5$ |
| 59.1-a1 |
59.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( 59^{2} \) |
$16.78124$ |
$(-2a^2+3a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.077131006$ |
$831.3314901$ |
4.547412191 |
\( -\frac{517531336}{3481} a^{3} - \frac{578018861}{3481} a^{2} + \frac{3430332701}{3481} a + \frac{4917997502}{3481} \) |
\( \bigl[a^{2} - 6\) , \( -a^{3} + 6 a + 5\) , \( 0\) , \( -a^{2} + 9 a - 15\) , \( 7 a^{3} - 32 a^{2} + 6 a + 79\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{3}+6a+5\right){x}^{2}+\left(-a^{2}+9a-15\right){x}+7a^{3}-32a^{2}+6a+79$ |
| 59.1-b1 |
59.1-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( 59^{2} \) |
$16.78124$ |
$(-2a^2+3a+12)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.026782869$ |
$768.1912666$ |
5.836433713 |
\( -\frac{7359978}{3481} a^{3} - \frac{6891655}{3481} a^{2} + \frac{63538298}{3481} a + \frac{98318070}{3481} \) |
\( \bigl[a^{3} - 7 a - 6\) , \( -a^{3} + 2 a^{2} + 5 a - 5\) , \( a^{3} - a^{2} - 5 a\) , \( -7 a^{3} + 3 a^{2} + 47 a + 31\) , \( -7 a^{3} - 8 a^{2} + 61 a + 94\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-5\right){x}^{2}+\left(-7a^{3}+3a^{2}+47a+31\right){x}-7a^{3}-8a^{2}+61a+94$ |
| 59.1-c1 |
59.1-c |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( 59 \) |
$16.78124$ |
$(-2a^2+3a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.090485788$ |
$947.0327135$ |
3.038620407 |
\( \frac{1711879}{59} a^{3} - \frac{6235467}{59} a^{2} - \frac{6976812}{59} a + \frac{30429034}{59} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + 5 a^{2} + 4 a - 27\) , \( -a^{3} + 8 a^{2} + 2 a - 43\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}-{x}^{2}+\left(-a^{3}+5a^{2}+4a-27\right){x}-a^{3}+8a^{2}+2a-43$ |
| 59.2-a1 |
59.2-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( 59^{2} \) |
$16.78124$ |
$(2a^2-a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.077131006$ |
$831.3314901$ |
4.547412191 |
\( \frac{517531336}{3481} a^{3} - \frac{2130612869}{3481} a^{2} - \frac{721700971}{3481} a + \frac{7252780006}{3481} \) |
\( \bigl[a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - 5\) , \( -19 a^{3} - 22 a^{2} + 124 a + 180\) , \( -275 a^{3} - 308 a^{2} + 1787 a + 2552\bigr] \) |
${y}^2+\left(a^{3}-6a-6\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-19a^{3}-22a^{2}+124a+180\right){x}-275a^{3}-308a^{2}+1787a+2552$ |
| 59.2-b1 |
59.2-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( 59^{2} \) |
$16.78124$ |
$(2a^2-a-13)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.026782869$ |
$768.1912666$ |
5.836433713 |
\( \frac{7359978}{3481} a^{3} - \frac{28971589}{3481} a^{2} - \frac{27675054}{3481} a + \frac{147604735}{3481} \) |
\( \bigl[a\) , \( a^{3} - 7 a - 6\) , \( a^{3} - 7 a - 5\) , \( 5 a^{3} + 5 a^{2} - 30 a - 38\) , \( -9 a^{3} - 10 a^{2} + 57 a + 80\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-7a-5\right){y}={x}^{3}+\left(a^{3}-7a-6\right){x}^{2}+\left(5a^{3}+5a^{2}-30a-38\right){x}-9a^{3}-10a^{2}+57a+80$ |
| 59.2-c1 |
59.2-c |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( 59 \) |
$16.78124$ |
$(2a^2-a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.090485788$ |
$947.0327135$ |
3.038620407 |
\( -\frac{1711879}{59} a^{3} - \frac{1099830}{59} a^{2} + \frac{14312109}{59} a + \frac{18928634}{59} \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 7 a - 7\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} - a^{2} + 7 a + 10\) , \( -a^{3} - 2 a^{2} + 7 a + 13\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-7a-7\right){x}^{2}+\left(-a^{3}-a^{2}+7a+10\right){x}-a^{3}-2a^{2}+7a+13$ |
| 61.1-a1 |
61.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
61.1 |
\( 61 \) |
\( 61^{2} \) |
$16.85131$ |
$(a^3-a^2-6a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$158.2188939$ |
2.805171670 |
\( \frac{106511209407}{3721} a^{3} - \frac{389010828845}{3721} a^{2} - \frac{422389790030}{3721} a + \frac{1869580634706}{3721} \) |
\( \bigl[a^{3} - 6 a - 6\) , \( -a^{2} + 5\) , \( a\) , \( 22 a^{3} - 95 a^{2} - 22 a + 320\) , \( 183 a^{3} - 754 a^{2} - 230 a + 2498\bigr] \) |
${y}^2+\left(a^{3}-6a-6\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(22a^{3}-95a^{2}-22a+320\right){x}+183a^{3}-754a^{2}-230a+2498$ |
| 61.1-b1 |
61.1-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
61.1 |
\( 61 \) |
\( 61^{4} \) |
$16.85131$ |
$(a^3-a^2-6a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.126800216$ |
$242.9821026$ |
4.370039547 |
\( -\frac{12187418446714}{13845841} a^{3} - \frac{30698902576403}{13845841} a^{2} + \frac{88314032441990}{13845841} a + \frac{209122732135322}{13845841} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( a^{3} - a^{2} - 5 a\) , \( -5 a^{3} + 14 a^{2} + 15 a - 41\) , \( 3 a^{3} - 15 a^{2} + 5 a + 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-5a^{3}+14a^{2}+15a-41\right){x}+3a^{3}-15a^{2}+5a+33$ |
| 61.2-a1 |
61.2-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
61.2 |
\( 61 \) |
\( 61^{2} \) |
$16.85131$ |
$(a^3-2a^2-5a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$158.2188939$ |
2.805171670 |
\( -\frac{106511209407}{3721} a^{3} - \frac{69477200624}{3721} a^{2} + \frac{880877819499}{3721} a + \frac{1164691225238}{3721} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + 6 a + 5\) , \( a + 1\) , \( -24 a^{3} - 26 a^{2} + 155 a + 219\) , \( -183 a^{3} - 205 a^{2} + 1188 a + 1697\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+6a+5\right){x}^{2}+\left(-24a^{3}-26a^{2}+155a+219\right){x}-183a^{3}-205a^{2}+1188a+1697$ |
| 61.2-b1 |
61.2-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
61.2 |
\( 61 \) |
\( 61^{4} \) |
$16.85131$ |
$(a^3-2a^2-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.126800216$ |
$242.9821026$ |
4.370039547 |
\( \frac{12187418446714}{13845841} a^{3} - \frac{67261157916545}{13845841} a^{2} + \frac{9646028050958}{13845841} a + \frac{254550443554195}{13845841} \) |
\( \bigl[a\) , \( -a^{2} + a + 7\) , \( a^{3} - 6 a - 5\) , \( 3 a^{3} + 2 a^{2} - 19 a - 22\) , \( -4 a^{3} - 5 a^{2} + 20 a + 26\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(3a^{3}+2a^{2}-19a-22\right){x}-4a^{3}-5a^{2}+20a+26$ |
| 71.1-a1 |
71.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{2} \) |
$17.17413$ |
$(a^3-5a^2-a+22)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.024689927$ |
$2310.866053$ |
4.046277582 |
\( \frac{2577873677}{5041} a^{3} - \frac{9941997472}{5041} a^{2} - \frac{9728711645}{5041} a + \frac{48667337706}{5041} \) |
\( \bigl[a^{3} - 7 a - 6\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - 7 a - 5\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 7 a + 6\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{3}-7a-5\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-a^{3}+a^{2}+5a\right){x}-a^{3}+7a+6$ |
| 71.1-b1 |
71.1-b |
$2$ |
$2$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{6} \) |
$17.17413$ |
$(a^3-5a^2-a+22)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \cdot 3 \) |
$1$ |
$116.7132163$ |
4.438988757 |
\( -\frac{4821712771898949793340}{128100283921} a^{3} + \frac{19885470844258087262355}{128100283921} a^{2} + \frac{6064859124809959355995}{128100283921} a - \frac{66008970295200178045822}{128100283921} \) |
\( \bigl[a^{3} - 7 a - 6\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{3} - 7 a - 6\) , \( -250 a^{3} + 882 a^{2} + 1045 a - 4256\) , \( 5147 a^{3} - 18820 a^{2} - 20494 a + 90808\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{3}-7a-6\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(-250a^{3}+882a^{2}+1045a-4256\right){x}+5147a^{3}-18820a^{2}-20494a+90808$ |
| 71.1-b2 |
71.1-b |
$2$ |
$2$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{3} \) |
$17.17413$ |
$(a^3-5a^2-a+22)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 3 \) |
$1$ |
$466.8528655$ |
4.438988757 |
\( \frac{53410583597570540}{357911} a^{3} - \frac{195066163020420255}{357911} a^{2} - \frac{211817431649546545}{357911} a + \frac{937481300471411793}{357911} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{3} - 7 a - 6\) , \( -34 a^{3} + 117 a^{2} + 154 a - 575\) , \( 276 a^{3} - 996 a^{2} - 1138 a + 4873\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-7a-6\right){y}={x}^{3}+a{x}^{2}+\left(-34a^{3}+117a^{2}+154a-575\right){x}+276a^{3}-996a^{2}-1138a+4873$ |
| 71.2-a1 |
71.2-a |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( - 71^{3} \) |
$17.17413$ |
$(a^3-3a^2-4a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$5.969538367$ |
1.905084980 |
\( \frac{471477927140188160}{357911} a^{3} - \frac{1721963035357900800}{357911} a^{2} - \frac{1869786284821422080}{357911} a + \frac{8275721449490710528}{357911} \) |
\( \bigl[0\) , \( a^{2} - a - 6\) , \( a\) , \( 5 a^{3} - a^{2} - 62 a - 80\) , \( -872 a^{3} - 593 a^{2} + 7120 a + 9448\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(5a^{3}-a^{2}-62a-80\right){x}-872a^{3}-593a^{2}+7120a+9448$ |
| 71.2-a2 |
71.2-a |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( -71 \) |
$17.17413$ |
$(a^3-3a^2-4a+10)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$483.5326077$ |
1.905084980 |
\( \frac{372957184}{71} a^{3} + \frac{242479104}{71} a^{2} - \frac{3083681792}{71} a - \frac{4072980480}{71} \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - a^{2} - 6 a + 1\) , \( -2 a^{3} + 14 a^{2} - 3 a - 54\) , \( 45 a^{3} - 182 a^{2} - 59 a + 595\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-2a^{3}+14a^{2}-3a-54\right){x}+45a^{3}-182a^{2}-59a+595$ |
| 71.2-b1 |
71.2-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.2 |
\( 71 \) |
\( -71 \) |
$17.17413$ |
$(a^3-3a^2-4a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.062799766$ |
$1844.017254$ |
4.106332450 |
\( \frac{8294400}{71} a^{3} - \frac{33832960}{71} a^{2} - \frac{30965760}{71} a + \frac{163565568}{71} \) |
\( \bigl[0\) , \( a^{2} - 2 a - 6\) , \( a\) , \( 3 a^{3} - a^{2} - 20 a - 17\) , \( -10 a^{3} - 5 a^{2} + 80 a + 100\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(3a^{3}-a^{2}-20a-17\right){x}-10a^{3}-5a^{2}+80a+100$ |
| 71.3-a1 |
71.3-a |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( - 71^{3} \) |
$17.17413$ |
$(2a^2-a-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$5.969538367$ |
1.905084980 |
\( -\frac{471477927140188160}{357911} a^{3} - \frac{307529253937336320}{357911} a^{2} + \frac{3899278574116659200}{357911} a + \frac{5155450056451575808}{357911} \) |
\( \bigl[0\) , \( a^{2} - a - 6\) , \( a + 1\) , \( -5 a^{3} + 14 a^{2} + 49 a - 138\) , \( 872 a^{3} - 3209 a^{2} - 3319 a + 15103\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-5a^{3}+14a^{2}+49a-138\right){x}+872a^{3}-3209a^{2}-3319a+15103$ |
| 71.3-a2 |
71.3-a |
$2$ |
$3$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( -71 \) |
$17.17413$ |
$(2a^2-a-9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$483.5326077$ |
1.905084980 |
\( -\frac{372957184}{71} a^{3} + \frac{1361350656}{71} a^{2} + \frac{1479852032}{71} a - \frac{6541225984}{71} \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 7 a - 5\) , \( 18 a^{3} + 21 a^{2} - 116 a - 167\) , \( -760 a^{3} - 852 a^{2} + 4940 a + 7059\bigr] \) |
${y}^2+\left(a^{3}-7a-5\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-1\right){x}^{2}+\left(18a^{3}+21a^{2}-116a-167\right){x}-760a^{3}-852a^{2}+4940a+7059$ |
| 71.3-b1 |
71.3-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.3 |
\( 71 \) |
\( -71 \) |
$17.17413$ |
$(2a^2-a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.062799766$ |
$1844.017254$ |
4.106332450 |
\( -\frac{8294400}{71} a^{3} - \frac{8949760}{71} a^{2} + \frac{73748480}{71} a + \frac{107061248}{71} \) |
\( \bigl[0\) , \( a^{2} - 7\) , \( a + 1\) , \( -3 a^{3} + 8 a^{2} + 13 a - 35\) , \( 10 a^{3} - 35 a^{2} - 41 a + 165\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-3a^{3}+8a^{2}+13a-35\right){x}+10a^{3}-35a^{2}-41a+165$ |
| 71.4-a1 |
71.4-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.4 |
\( 71 \) |
\( 71^{2} \) |
$17.17413$ |
$(-2a^3-2a^2+13a+19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.024689927$ |
$2310.866053$ |
4.046277582 |
\( -\frac{2577873677}{5041} a^{3} - \frac{2208376441}{5041} a^{2} + \frac{21879085558}{5041} a + \frac{31574502266}{5041} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 7\) , \( a\) , \( 4 a^{3} + a^{2} - 23 a - 21\) , \( 5 a^{3} + 6 a^{2} - 33 a - 49\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+7\right){x}^{2}+\left(4a^{3}+a^{2}-23a-21\right){x}+5a^{3}+6a^{2}-33a-49$ |
| 71.4-b1 |
71.4-b |
$2$ |
$2$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.4 |
\( 71 \) |
\( - 71^{3} \) |
$17.17413$ |
$(-2a^3-2a^2+13a+19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.357529315$ |
$466.8528655$ |
4.438988757 |
\( -\frac{53410583597570540}{357911} a^{3} - \frac{34834412227708635}{357911} a^{2} + \frac{441718006897675435}{357911} a + \frac{584008289399015533}{357911} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{3} - 7 a - 6\) , \( 32 a^{3} + 18 a^{2} - 271 a - 351\) , \( -222 a^{3} - 142 a^{2} + 1846 a + 2436\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-7a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(32a^{3}+18a^{2}-271a-351\right){x}-222a^{3}-142a^{2}+1846a+2436$ |
| 71.4-b2 |
71.4-b |
$2$ |
$2$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
71.4 |
\( 71 \) |
\( - 71^{6} \) |
$17.17413$ |
$(-2a^3-2a^2+13a+19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.715058630$ |
$116.7132163$ |
4.438988757 |
\( \frac{4821712771898949793340}{128100283921} a^{3} + \frac{5420332528561237882335}{128100283921} a^{2} - \frac{31370662497629284500685}{128100283921} a - \frac{44880353098031081220812}{128100283921} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{3} - 7 a - 6\) , \( -33 a^{3} - 62 a^{2} + 159 a + 284\) , \( 451 a^{3} + 604 a^{2} - 2522 a - 3781\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-7a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-33a^{3}-62a^{2}+159a+284\right){x}+451a^{3}+604a^{2}-2522a-3781$ |
| 81.1-a1 |
81.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{4} \) |
$17.45935$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$284.3489357$ |
2.520708998 |
\( -233186171 a^{3} - \frac{784011394}{3} a^{2} + \frac{4549013683}{3} a + \frac{6500951017}{3} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{3} - 7 a - 5\) , \( -2 a^{3} + 4 a^{2} + 8 a - 9\) , \( -a^{3} + 2 a^{2} + 3 a - 6\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-7a-5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(-2a^{3}+4a^{2}+8a-9\right){x}-a^{3}+2a^{2}+3a-6$ |
| 81.1-b1 |
81.1-b |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( - 3^{4} \) |
$17.45935$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$274.1121562$ |
2.429961542 |
\( -\frac{49070}{3} a^{3} + \frac{196240}{3} a^{2} + 79610 a - 373117 \) |
\( \bigl[a^{3} - 7 a - 6\) , \( a + 1\) , \( a^{3} - a^{2} - 6 a + 1\) , \( 3 a^{3} - 26 a^{2} + 19 a + 110\) , \( 15 a^{3} - 82 a^{2} + 13 a + 307\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{3}-a^{2}-6a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a^{3}-26a^{2}+19a+110\right){x}+15a^{3}-82a^{2}+13a+307$ |
| 81.1-c1 |
81.1-c |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( - 3^{4} \) |
$17.45935$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$274.1121562$ |
2.429961542 |
\( \frac{49070}{3} a^{3} + \frac{49030}{3} a^{2} - \frac{484100}{3} a - \frac{733351}{3} \) |
\( \bigl[a\) , \( -a^{3} + 7 a + 5\) , \( a + 1\) , \( -46 a^{3} - 51 a^{2} + 301 a + 428\) , \( -379 a^{3} - 425 a^{2} + 2466 a + 3526\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+7a+5\right){x}^{2}+\left(-46a^{3}-51a^{2}+301a+428\right){x}-379a^{3}-425a^{2}+2466a+3526$ |
| 81.1-d1 |
81.1-d |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{4} \) |
$17.45935$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$284.3489357$ |
2.520708998 |
\( 233186171 a^{3} - \frac{2882686933}{3} a^{2} - \frac{882315356}{3} a + \frac{9566394793}{3} \) |
\( \bigl[a^{3} - 6 a - 6\) , \( -a + 1\) , \( a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 8 a - 3\) , \( a^{3} - a^{2} - 5 a - 1\bigr] \) |
${y}^2+\left(a^{3}-6a-6\right){x}{y}+\left(a^{3}-a^{2}-6a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a^{3}-8a-3\right){x}+a^{3}-a^{2}-5a-1$ |
| 121.1-a1 |
121.1-a |
$1$ |
$1$ |
4.4.12725.1 |
$4$ |
$[4, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$18.35759$ |
$(-a^3+6a+4), (a^2-2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.032825304$ |
$816.5452672$ |
3.801719946 |
\( \frac{41622059604}{121} a^{3} - \frac{152012863297}{121} a^{2} - \frac{165065371815}{121} a + \frac{730570104901}{121} \) |
\( \bigl[a^{2} - a - 5\) , \( -1\) , \( a^{2} - a - 5\) , \( 10 a^{3} + 10 a^{2} - 67 a - 93\) , \( 33 a^{3} + 36 a^{2} - 217 a - 308\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}-{x}^{2}+\left(10a^{3}+10a^{2}-67a-93\right){x}+33a^{3}+36a^{2}-217a-308$ |
*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.
