| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$10.39028$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$392.2876592$ |
0.483800168 |
\( -\frac{162598523}{6561} a^{3} + \frac{1076455574}{6561} a^{2} + \frac{11814862}{2187} a - \frac{446414915}{6561} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 3 a^{2} + a - 2\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -16 a^{3} + 42 a^{2} + 52 a - 47\) , \( -23 a^{3} + 60 a^{2} + 79 a - 74\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-2\right){x}^{2}+\left(-16a^{3}+42a^{2}+52a-47\right){x}-23a^{3}+60a^{2}+79a-74$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$10.39028$ |
$(-a^2+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$392.2876592$ |
0.483800168 |
\( -\frac{490913}{81} a^{3} + \frac{614549}{81} a^{2} + \frac{986851}{27} a + \frac{1612993}{81} \) |
\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 4 a^{3} - 5 a^{2} - 25 a - 12\) , \( -10 a^{3} + 14 a^{2} + 57 a + 26\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(4a^{3}-5a^{2}-25a-12\right){x}-10a^{3}+14a^{2}+57a+26$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{32} \) |
$10.39028$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$98.07191480$ |
0.483800168 |
\( -\frac{65801148718729342433}{1853020188851841} a^{3} + \frac{241347061408650362369}{1853020188851841} a^{2} + \frac{6433207753084724497}{617673396283947} a - \frac{104140064860404663251}{1853020188851841} \) |
\( \bigl[a + 1\) , \( a^{2} - 3 a - 3\) , \( 2 a^{3} - 5 a^{2} - 5 a + 3\) , \( -a^{3} - 2 a^{2} + 3\) , \( 75 a^{3} - 192 a^{2} - 243 a + 224\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{3}-5a^{2}-5a+3\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-a^{3}-2a^{2}+3\right){x}+75a^{3}-192a^{2}-243a+224$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$10.39028$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$24.51797870$ |
0.483800168 |
\( \frac{152107352927}{81} a^{3} + \frac{5079049960255}{81} a^{2} - \frac{77002114672}{27} a - \frac{2194982180275}{81} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 4\) , \( a\) , \( -138 a^{3} + 166 a^{2} + 853 a + 465\) , \( 1126 a^{3} - 1525 a^{2} - 6553 a - 3272\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-3a+4\right){x}^{2}+\left(-138a^{3}+166a^{2}+853a+465\right){x}+1126a^{3}-1525a^{2}-6553a-3272$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$10.39028$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$392.2876592$ |
0.483800168 |
\( -\frac{14302878060005}{43046721} a^{3} + \frac{18321260673233}{43046721} a^{2} + \frac{28525137795658}{14348907} a + \frac{45563531574361}{43046721} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 3\) , \( -a - 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( 5 a^{3} - 20 a^{2} - a + 4\) , \( 13 a^{3} - 49 a^{2} - 3 a + 18\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+3\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a^{3}-20a^{2}-a+4\right){x}+13a^{3}-49a^{2}-3a+18$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$10.39028$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$98.07191480$ |
0.483800168 |
\( -\frac{5611009081929727}{6561} a^{3} + \frac{7438171844716255}{6561} a^{2} + \frac{11025722829775055}{2187} a + \frac{16682927017038851}{6561} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 3\) , \( a\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 9 a^{3} + 5 a^{2} - 97 a - 65\) , \( 80 a^{3} - 105 a^{2} - 474 a - 240\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+3\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+a{x}^{2}+\left(9a^{3}+5a^{2}-97a-65\right){x}+80a^{3}-105a^{2}-474a-240$ |
| 4.1-a1 |
4.1-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$10.77072$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.012446468$ |
$1032.627104$ |
1.521676262 |
\( -430 a^{3} + 1241 a^{2} + 406 a - 1216 \) |
\( \bigl[a\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -2 a^{3} + 6 a^{2} + 6 a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-6a+4\right){x}^{2}+\left(a^{3}-3a^{2}-3a+5\right){x}-2a^{3}+6a^{2}+6a-9$ |
| 4.1-a2 |
4.1-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$10.77072$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.037339405$ |
$1032.627104$ |
1.521676262 |
\( 153136538 a^{3} - 147894105 a^{2} - 1052140329 a - 573351178 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 4\) , \( a + 1\) , \( a^{3} - 3 a^{2} - a + 4\) , \( 31 a^{3} - 43 a^{2} - 177 a - 83\) , \( -138 a^{3} + 178 a^{2} + 824 a + 432\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+4\right){x}{y}+\left(a^{3}-3a^{2}-a+4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(31a^{3}-43a^{2}-177a-83\right){x}-138a^{3}+178a^{2}+824a+432$ |
| 6.1-a1 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{24} \cdot 3^{2} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.160459024$ |
$539.5699589$ |
2.562621821 |
\( \frac{4261976946245}{150994944} a^{3} + \frac{785264011297}{9437184} a^{2} - \frac{815593843219}{50331648} a - \frac{5324733392509}{150994944} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( 4 a^{3} - 16 a^{2} + 5 a + 4\) , \( -16 a^{3} + 54 a^{2} + 8 a - 25\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(4a^{3}-16a^{2}+5a+4\right){x}-16a^{3}+54a^{2}+8a-25$ |
| 6.1-a2 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{4} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \cdot 3 \) |
$1.283672195$ |
$2.107695152$ |
2.562621821 |
\( -\frac{385907673357759089}{648} a^{3} + \frac{64030812003531643}{81} a^{2} + \frac{757786801964022655}{216} a + \frac{1145162494665993961}{648} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 4\) , \( a\) , \( -1696 a^{3} + 4393 a^{2} + 5547 a - 5214\) , \( -51605 a^{3} + 135167 a^{2} + 169861 a - 159958\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-1696a^{3}+4393a^{2}+5547a-5214\right){x}-51605a^{3}+135167a^{2}+169861a-159958$ |
| 6.1-a3 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{24} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1.925508293$ |
$33.72312243$ |
2.562621821 |
\( \frac{3781093546321912668949525}{1129718145924} a^{3} + \frac{1276282565912701214820329}{282429536481} a^{2} - \frac{600799457623047968962547}{376572715308} a - \frac{2257252737813493720757933}{1129718145924} \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 166 a^{3} - 566 a^{2} - 36 a + 229\) , \( -1758 a^{3} + 5944 a^{2} + 577 a - 2549\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(166a^{3}-566a^{2}-36a+229\right){x}-1758a^{3}+5944a^{2}+577a-2549$ |
| 6.1-a4 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{12} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \) |
$3.851016586$ |
$2.107695152$ |
2.562621821 |
\( \frac{601999727802116775763708540747759}{1062882} a^{3} + \frac{406401876987587082599717771104846}{531441} a^{2} - \frac{95655160412617646709739080945527}{354294} a - \frac{359384267689062052382384705780123}{1062882} \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 866 a^{3} - 2911 a^{2} - 361 a + 1269\) , \( 24287 a^{3} - 82213 a^{2} - 7661 a + 34963\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(866a^{3}-2911a^{2}-361a+1269\right){x}+24287a^{3}-82213a^{2}-7661a+34963$ |
| 6.1-a5 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{2} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.160459024$ |
$539.5699589$ |
2.562621821 |
\( -\frac{675101}{576} a^{3} + \frac{73019}{36} a^{2} + \frac{1142587}{192} a + \frac{1534357}{576} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 3 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( 2 a^{2} - 2 a - 3\) , \( -2 a^{3} + 4 a^{2} + 13 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a-1\right){x}^{2}+\left(2a^{2}-2a-3\right){x}-2a^{3}+4a^{2}+13a+3$ |
| 6.1-a6 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{12} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$0.962754146$ |
$539.5699589$ |
2.562621821 |
\( -\frac{20588156741795}{8503056} a^{3} + \frac{4924080939830}{531441} a^{2} + \frac{3179294002165}{2834352} a - \frac{31453924413269}{8503056} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a + 1\) , \( 8 a^{3} - 26 a^{2} - 27 a + 11\) , \( -11 a^{3} + 21 a + 23\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(8a^{3}-26a^{2}-27a+11\right){x}-11a^{3}+21a+23$ |
| 6.1-a7 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{48} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \) |
$3.851016586$ |
$2.107695152$ |
2.562621821 |
\( \frac{181874767870880530379510879201}{159532886153745019726722} a^{3} - \frac{322096036142823400798557877678}{79766443076872509863361} a^{2} - \frac{239185082631087268873272415705}{53177628717915006575574} a + \frac{720229498536874711870403693867}{159532886153745019726722} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a + 1\) , \( -42 a^{3} + 9 a^{2} + 88 a + 51\) , \( -371 a^{3} - 267 a^{2} + 214 a + 141\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(-42a^{3}+9a^{2}+88a+51\right){x}-371a^{3}-267a^{2}+214a+141$ |
| 6.1-a8 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{8} \cdot 3^{6} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.481377073$ |
$539.5699589$ |
2.562621821 |
\( -\frac{9200487182081236075}{186624} a^{3} + \frac{1945135925807017825}{11664} a^{2} + \frac{990294199118049725}{62208} a - \frac{13308299556016760653}{186624} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 3\) , \( -a - 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( 18 a^{3} - 47 a^{2} - 39 a - 22\) , \( -108 a^{3} + 203 a^{2} + 473 a + 197\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+3\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a^{3}-47a^{2}-39a-22\right){x}-108a^{3}+203a^{2}+473a+197$ |
| 6.1-a9 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.320918048$ |
$539.5699589$ |
2.562621821 |
\( \frac{9176249149}{331776} a^{3} - \frac{1539885895}{20736} a^{2} - \frac{9846620507}{110592} a + \frac{31212084043}{331776} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -a^{3} + 2 a^{2} + 3 a + 1\) , \( 1\) , \( -2 a^{3} + 5 a + 2\) , \( 8 a^{3} - 19 a^{2} - a + 9\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a+1\right){x}^{2}+\left(-2a^{3}+5a+2\right){x}+8a^{3}-19a^{2}-a+9$ |
| 6.1-a10 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{16} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \cdot 3 \) |
$1.283672195$ |
$2.107695152$ |
2.562621821 |
\( \frac{14228462704292045281028335457}{344373768} a^{3} - \frac{4697247873747489990741018571}{43046721} a^{2} - \frac{15684402499104234245841758095}{114791256} a + \frac{44391595847473673362427154983}{344373768} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -a^{3} + 2 a^{2} + 3 a + 1\) , \( 1\) , \( 13 a^{3} - 55 a^{2} + 35 a + 2\) , \( 153 a^{3} - 1450 a^{2} + 89 a + 553\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a+1\right){x}^{2}+\left(13a^{3}-55a^{2}+35a+2\right){x}+153a^{3}-1450a^{2}+89a+553$ |
| 6.1-a11 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$0.641836097$ |
$33.72312243$ |
2.562621821 |
\( \frac{1364399679792661}{419904} a^{3} - \frac{225523988109655}{26244} a^{2} - \frac{1500808881322883}{139968} a + \frac{4280137372942003}{419904} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -a^{3} + 2 a^{2} + 3 a + 1\) , \( 1\) , \( 23 a^{3} - 120 a^{2} + 52\) , \( 241 a^{3} - 1119 a^{2} - 64 a + 479\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a+1\right){x}^{2}+\left(23a^{3}-120a^{2}+52\right){x}+241a^{3}-1119a^{2}-64a+479$ |
| 6.1-a12 |
6.1-a |
$12$ |
$24$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{6} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.481377073$ |
$539.5699589$ |
2.562621821 |
\( -\frac{108603924706205}{2916} a^{3} + \frac{36014869276394}{729} a^{2} + \frac{213349500053983}{972} a + \frac{322490108152957}{2916} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( a^{3} - 3 a^{2} - a + 2\) , \( a^{3} - 2 a^{2} - 3 a\) , \( 26 a^{3} - 69 a^{2} - 84 a + 80\) , \( 1362 a^{3} - 3597 a^{2} - 4504 a + 4248\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+2\right){x}^{2}+\left(26a^{3}-69a^{2}-84a+80\right){x}+1362a^{3}-3597a^{2}-4504a+4248$ |
| 6.1-b1 |
6.1-b |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{12} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$97.98210701$ |
0.966714271 |
\( -\frac{4524688200125}{34012224} a^{3} - \frac{370599297793}{2125764} a^{2} + \frac{837482354971}{11337408} a + \frac{2907844519861}{34012224} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{2} + 3 a + 2\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( -3 a^{3} + 10 a^{2} + a - 9\) , \( 2 a^{3} - 8 a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+3a+2\right){x}^{2}+\left(-3a^{3}+10a^{2}+a-9\right){x}+2a^{3}-8a^{2}+a$ |
| 6.1-b2 |
6.1-b |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{6} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$97.98210701$ |
0.966714271 |
\( \frac{2593304734091984021}{2985984} a^{3} + \frac{218838120295109425}{186624} a^{2} - \frac{412064939102013763}{995328} a - \frac{1548161697177706573}{2985984} \) |
\( \bigl[1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -5 a^{3} + 5 a^{2} + 36 a + 17\) , \( -71 a^{3} + 91 a^{2} + 426 a + 216\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(-5a^{3}+5a^{2}+36a+17\right){x}-71a^{3}+91a^{2}+426a+216$ |
| 6.1-b3 |
6.1-b |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{2} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$97.98210701$ |
0.966714271 |
\( -\frac{3832187515}{144} a^{3} + \frac{863777635}{9} a^{2} - \frac{736893475}{48} a - \frac{3609734941}{144} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 3\) , \( -a^{2} + 2 a + 4\) , \( a + 1\) , \( -12 a^{2} + 2 a + 21\) , \( -5 a^{3} - 22 a^{2} + a + 20\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-12a^{2}+2a+21\right){x}-5a^{3}-22a^{2}+a+20$ |
| 6.1-b4 |
6.1-b |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{4} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$97.98210701$ |
0.966714271 |
\( -\frac{9980525}{324} a^{3} + \frac{3095225}{81} a^{2} + \frac{20513275}{108} a + \frac{30152197}{324} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -a\) , \( 2 a^{3} - 5 a^{2} - 5 a + 3\) , \( -39 a^{3} + 102 a^{2} + 129 a - 120\) , \( -230 a^{3} + 607 a^{2} + 760 a - 718\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+\left(2a^{3}-5a^{2}-5a+3\right){y}={x}^{3}-a{x}^{2}+\left(-39a^{3}+102a^{2}+129a-120\right){x}-230a^{3}+607a^{2}+760a-718$ |
| 6.1-c1 |
6.1-c |
$2$ |
$2$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{4} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.018157087$ |
$1317.871567$ |
1.888689767 |
\( -\frac{520577}{324} a^{3} - \frac{165451}{81} a^{2} + \frac{183583}{108} a + \frac{649021}{324} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 2 a^{3} - 5 a^{2} - 5 a + 3\) , \( 2 a^{3} - 8 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+3\right){x}{y}+\left(2a^{3}-5a^{2}-5a+3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+2\right){x}^{2}+\left(2a^{3}-8a^{2}-6a+5\right){x}+2a^{3}-5a^{2}-5a+4$ |
| 6.1-c2 |
6.1-c |
$2$ |
$2$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{2} \) |
$11.33068$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.036314175$ |
$1317.871567$ |
1.888689767 |
\( \frac{16614900725}{144} a^{3} + \frac{1402610737}{9} a^{2} - \frac{2640248275}{48} a - \frac{9922138333}{144} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -8 a^{3} + 21 a^{2} + 30 a - 26\) , \( -26 a^{3} + 68 a^{2} + 87 a - 82\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+3\right){x}{y}+\left(2a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(-8a^{3}+21a^{2}+30a-26\right){x}-26a^{3}+68a^{2}+87a-82$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$11.74555$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.035116035$ |
$298.4403527$ |
1.654376528 |
\( -\frac{549255}{8} a^{3} - \frac{2302503}{16} a^{2} - \frac{1281605}{8} a - 61432 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a\) , \( -a - 1\) , \( 2 a^{3} - 5 a^{2} - 5 a + 3\) , \( 3 a^{3} - 10 a^{2} - 9 a + 7\) , \( 8 a^{3} - 22 a^{2} - 23 a + 22\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a\right){x}{y}+\left(2a^{3}-5a^{2}-5a+3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a^{3}-10a^{2}-9a+7\right){x}+8a^{3}-22a^{2}-23a+22$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{36} \) |
$11.74555$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.011705345$ |
$298.4403527$ |
1.654376528 |
\( -\frac{727264585}{4096} a^{3} + \frac{1938914411}{4096} a^{2} + \frac{2331132925}{4096} a - \frac{1112683511}{2048} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{3} + 2 a^{2} + 5 a + 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( -20 a^{3} + 54 a^{2} + 74 a - 55\) , \( 34 a^{3} - 85 a^{2} - 106 a + 105\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+4\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a+1\right){x}^{2}+\left(-20a^{3}+54a^{2}+74a-55\right){x}+34a^{3}-85a^{2}-106a+105$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$11.74555$ |
$(a^3-2a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.008486035$ |
$2124.058975$ |
1.422698135 |
\( -\frac{32003}{2} a^{3} + \frac{205437}{4} a^{2} + \frac{10201}{2} a - 21666 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 4\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( 10 a^{3} - 35 a^{2} + a + 17\) , \( -27 a^{3} + 90 a^{2} + 9 a - 38\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+4\right){x}{y}+\left(a^{3}-2a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(10a^{3}-35a^{2}+a+17\right){x}-27a^{3}+90a^{2}+9a-38$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$11.74555$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$66.57198925$ |
2.627258959 |
\( 3951491 a^{3} - 5089040 a^{2} - 23590528 a - 12429848 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -2 a^{3} + 5 a^{2} + 7 a - 2\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -5 a^{3} + 19 a^{2} + 10 a - 27\) , \( 17 a^{2} - 22 a - 54\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+4\right){x}{y}+\left(2a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-2\right){x}^{2}+\left(-5a^{3}+19a^{2}+10a-27\right){x}+17a^{2}-22a-54$ |
| 9.1-a1 |
9.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$11.91976$ |
$(-a^2+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$312.1706310$ |
1.657952696 |
\( -\frac{14302878060005}{43046721} a^{3} + \frac{18321260673233}{43046721} a^{2} + \frac{28525137795658}{14348907} a + \frac{45563531574361}{43046721} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -25 a^{3} + 64 a^{2} + 80 a - 78\) , \( -159 a^{3} + 419 a^{2} + 524 a - 497\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+4\right){x}^{2}+\left(-25a^{3}+64a^{2}+80a-78\right){x}-159a^{3}+419a^{2}+524a-497$ |
| 9.1-a2 |
9.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{38} \) |
$11.91976$ |
$(-a^2+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{2} \) |
$1$ |
$39.02132888$ |
1.657952696 |
\( -\frac{65801148718729342433}{1853020188851841} a^{3} + \frac{241347061408650362369}{1853020188851841} a^{2} + \frac{6433207753084724497}{617673396283947} a - \frac{104140064860404663251}{1853020188851841} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -21 a^{2} - 15 a + 17\) , \( -284 a^{3} + 883 a^{2} + 1033 a - 1012\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+4\right){x}^{2}+\left(-21a^{2}-15a+17\right){x}-284a^{3}+883a^{2}+1033a-1012$ |
| 9.1-a3 |
9.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$11.91976$ |
$(-a^2+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{2} \) |
$1$ |
$312.1706310$ |
1.657952696 |
\( -\frac{490913}{81} a^{3} + \frac{614549}{81} a^{2} + \frac{986851}{27} a + \frac{1612993}{81} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 3\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( 0\) , \( -2 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{3} + 5 a^{2} - 3 a - 4\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+3\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a\right){x}^{2}+\left(-2a^{3}+7a^{2}+2a-1\right){x}-a^{3}+5a^{2}-3a-4$ |
| 9.1-a4 |
9.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$11.91976$ |
$(-a^2+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$624.3412621$ |
1.657952696 |
\( -\frac{162598523}{6561} a^{3} + \frac{1076455574}{6561} a^{2} + \frac{11814862}{2187} a - \frac{446414915}{6561} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 3 a^{2} - a + 3\) , \( 5 a^{3} - 9 a^{2} - 22 a - 13\) , \( -12 a^{3} + 16 a^{2} + 70 a + 34\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+3\right){x}{y}+\left(a^{3}-3a^{2}-a+3\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(5a^{3}-9a^{2}-22a-13\right){x}-12a^{3}+16a^{2}+70a+34$ |
| 9.1-a5 |
9.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$11.91976$ |
$(-a^2+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$156.0853155$ |
1.657952696 |
\( \frac{152107352927}{81} a^{3} + \frac{5079049960255}{81} a^{2} - \frac{77002114672}{27} a - \frac{2194982180275}{81} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 3 a^{2} - a + 3\) , \( 5 a^{3} - 54 a^{2} + 103 a + 72\) , \( -124 a^{3} + 375 a^{2} + 155 a - 70\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+3\right){x}{y}+\left(a^{3}-3a^{2}-a+3\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(5a^{3}-54a^{2}+103a+72\right){x}-124a^{3}+375a^{2}+155a-70$ |
| 9.1-a6 |
9.1-a |
$6$ |
$8$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$11.91976$ |
$(-a^2+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$78.04265776$ |
1.657952696 |
\( -\frac{5611009081929727}{6561} a^{3} + \frac{7438171844716255}{6561} a^{2} + \frac{11025722829775055}{2187} a + \frac{16682927017038851}{6561} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -a + 1\) , \( 1\) , \( -45 a^{3} + 156 a^{2} + 6 a - 75\) , \( -104 a^{3} + 346 a^{2} + 51 a - 144\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-45a^{3}+156a^{2}+6a-75\right){x}-104a^{3}+346a^{2}+51a-144$ |
| 12.1-a1 |
12.1-a |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{6} \) |
$12.35620$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.180527229$ |
$597.1927400$ |
2.127348242 |
\( -\frac{82012674512}{729} a^{3} + \frac{216490672625}{729} a^{2} + \frac{90475703044}{243} a - \frac{255370359212}{729} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -9 a^{3} + 33 a^{2} - 16\) , \( -29 a^{3} + 90 a^{2} + 8 a - 40\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+2\right){x}^{2}+\left(-9a^{3}+33a^{2}-16\right){x}-29a^{3}+90a^{2}+8a-40$ |
| 12.1-a2 |
12.1-a |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$12.35620$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.120351486$ |
$597.1927400$ |
2.127348242 |
\( -\frac{15800836}{3} a^{3} + \frac{23126023}{3} a^{2} + 28972549 a + \frac{43782902}{3} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 4\) , \( a^{2} - a - 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( -8 a^{3} + 48 a^{2} - 25 a - 150\) , \( 171 a^{3} - 352 a^{2} - 761 a + 71\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+4\right){x}{y}+\left(2a^{3}-5a^{2}-6a+4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-8a^{3}+48a^{2}-25a-150\right){x}+171a^{3}-352a^{2}-761a+71$ |
| 12.1-a3 |
12.1-a |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{2} \) |
$12.35620$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.060175743$ |
$597.1927400$ |
2.127348242 |
\( -\frac{7556}{9} a^{3} + \frac{7802}{9} a^{2} + \frac{17017}{3} a + \frac{25378}{9} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( a^{3} - 2 a^{2} - 3 a\) , \( a^{3} - 3 a^{2} - a + 4\) , \( a^{3} - 2 a^{2} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+\left(a^{3}-2a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a\right){x}^{2}+\left(a^{3}-3a^{2}-a+4\right){x}+a^{3}-2a^{2}-3a+1$ |
| 12.1-a4 |
12.1-a |
$4$ |
$6$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{3} \) |
$12.35620$ |
$(a), (-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.361054459$ |
$597.1927400$ |
2.127348242 |
\( \frac{1326997871092400600}{27} a^{3} - \frac{3504658547026792832}{27} a^{2} - \frac{1462784079926585563}{9} a + \frac{4140120714954152498}{27} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( 1\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -2 a^{3} - 6 a^{2} + 55 a - 34\) , \( 5 a^{3} + 10 a^{2} - 109 a + 67\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+{x}^{2}+\left(-2a^{3}-6a^{2}+55a-34\right){x}+5a^{3}+10a^{2}-109a+67$ |
| 13.1-a1 |
13.1-a |
$4$ |
$4$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$12.48045$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$643.1589456$ |
1.586388961 |
\( \frac{1813516}{13} a^{3} + \frac{2577448}{13} a^{2} - \frac{869212}{13} a - \frac{1139023}{13} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( -a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(a^{3}-3a^{2}-2a+3\right){x}-a$ |
| 13.1-a2 |
13.1-a |
$4$ |
$4$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( -13 \) |
$12.48045$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$643.1589456$ |
1.586388961 |
\( -\frac{76644782359934558}{13} a^{3} + \frac{259263489400797086}{13} a^{2} + \frac{24749810206588096}{13} a - \frac{110865435637822747}{13} \) |
\( \bigl[a + 1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -21 a^{3} + 55 a^{2} + 74 a - 58\) , \( 14 a^{3} - 36 a^{2} - 44 a + 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-2\right){x}^{2}+\left(-21a^{3}+55a^{2}+74a-58\right){x}+14a^{3}-36a^{2}-44a+45$ |
| 13.1-a3 |
13.1-a |
$4$ |
$4$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{4} \) |
$12.48045$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$321.5794728$ |
1.586388961 |
\( -\frac{99691899191446}{28561} a^{3} - \frac{135947950240950}{28561} a^{2} + \frac{1115184819296060}{28561} a + \frac{1538306924355827}{28561} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -2 a^{3} + 5 a^{2} + 5 a - 2\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( 1120 a^{3} - 1478 a^{2} - 6626 a - 3350\) , \( 40401 a^{3} - 53578 a^{2} - 238123 a - 119991\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-2\right){x}^{2}+\left(1120a^{3}-1478a^{2}-6626a-3350\right){x}+40401a^{3}-53578a^{2}-238123a-119991$ |
| 13.1-a4 |
13.1-a |
$4$ |
$4$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13^{2} \) |
$12.48045$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1286.317891$ |
1.586388961 |
\( -\frac{4829510968}{169} a^{3} + \frac{16328700860}{169} a^{2} + \frac{1574007648}{169} a - \frac{6944974927}{169} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( -2 a^{3} + 5 a^{2} + 5 a - 2\) , \( 2 a^{3} - 5 a^{2} - 6 a + 3\) , \( 65 a^{3} - 78 a^{2} - 406 a - 215\) , \( 685 a^{3} - 898 a^{2} - 4065 a - 2061\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+\left(2a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-2\right){x}^{2}+\left(65a^{3}-78a^{2}-406a-215\right){x}+685a^{3}-898a^{2}-4065a-2061$ |
| 16.2-a1 |
16.2-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$12.80862$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.087800837$ |
$312.8919177$ |
2.168374775 |
\( 153136538 a^{3} - 147894105 a^{2} - 1052140329 a - 573351178 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( 6 a^{3} - 10 a^{2} - 30 a - 12\) , \( -6 a^{3} + 7 a^{2} + 38 a + 20\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(6a^{3}-10a^{2}-30a-12\right){x}-6a^{3}+7a^{2}+38a+20$ |
| 16.2-a2 |
16.2-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$12.80862$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.029266945$ |
$938.6757531$ |
2.168374775 |
\( -430 a^{3} + 1241 a^{2} + 406 a - 1216 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 4\) , \( a\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( a^{3} + a^{2} + 2 a - 1\) , \( 2 a^{3} + a^{2} - a - 1\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+4\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+a{x}^{2}+\left(a^{3}+a^{2}+2a-1\right){x}+2a^{3}+a^{2}-a-1$ |
| 16.2-b1 |
16.2-b |
$1$ |
$1$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$12.80862$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$340.2185073$ |
3.356674975 |
\( 3951491 a^{3} - 5089040 a^{2} - 23590528 a - 12429848 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a\) , \( -a^{2} + 2 a + 4\) , \( a\) , \( -3 a^{2} + 9 a + 7\) , \( -a^{3} + 4 a^{2} - 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-3a^{2}+9a+7\right){x}-a^{3}+4a^{2}-2$ |
| 17.1-a1 |
17.1-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$12.90605$ |
$(a^3-3a^2-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$565.9666266$ |
1.240879657 |
\( -\frac{1626460689770}{289} a^{3} + \frac{4295555220733}{289} a^{2} + \frac{5378661502490}{289} a - \frac{5074423126968}{289} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 2\) , \( 1\) , \( 8 a^{3} - 22 a^{2} - 19 a + 22\) , \( 7 a^{3} - 19 a^{2} - 18 a + 19\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+4\right){x}{y}+{y}={x}^{3}+\left(2a^{3}-5a^{2}-5a+2\right){x}^{2}+\left(8a^{3}-22a^{2}-19a+22\right){x}+7a^{3}-19a^{2}-18a+19$ |
| 17.1-a2 |
17.1-a |
$2$ |
$3$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{6} \) |
$12.90605$ |
$(a^3-3a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$6.987242303$ |
1.240879657 |
\( -\frac{191315830244144862182}{24137569} a^{3} + \frac{646690509719075642103}{24137569} a^{2} + \frac{61794059323633745115}{24137569} a - \frac{276533821462642999698}{24137569} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 2\) , \( 1\) , \( 253 a^{3} - 857 a^{2} - 94 a + 382\) , \( 3725 a^{3} - 12618 a^{2} - 1222 a + 5406\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+4\right){x}{y}+{y}={x}^{3}+\left(2a^{3}-5a^{2}-5a+2\right){x}^{2}+\left(253a^{3}-857a^{2}-94a+382\right){x}+3725a^{3}-12618a^{2}-1222a+5406$ |
| 17.1-b1 |
17.1-b |
$1$ |
$1$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$12.90605$ |
$(a^3-3a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.023484358$ |
$1324.737739$ |
2.455556597 |
\( -\frac{479012569}{289} a^{3} + \frac{2248360031}{289} a^{2} - \frac{1546718592}{289} a - \frac{2041604532}{289} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{2} + a + 3\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( 5 a^{3} - 15 a^{2} - 8 a + 15\) , \( 3 a^{3} - 6 a^{2} - 10 a + 10\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+4\right){x}{y}+\left(a^{3}-3a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(5a^{3}-15a^{2}-8a+15\right){x}+3a^{3}-6a^{2}-10a+10$ |
*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.
