| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$73.36913734$ |
3.139270437 |
\( \frac{309494297}{64} a^{2} - \frac{1103588115}{64} a + \frac{709886159}{64} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - 5\) , \( 21 a^{2} - 5 a - 148\) , \( -80 a^{2} + 12 a + 571\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(21a^{2}-5a-148\right){x}-80a^{2}+12a+571$ |
| 2.1-a2 |
2.1-a |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$146.7382746$ |
3.139270437 |
\( -\frac{96991897}{8} a^{2} + \frac{15429267}{8} a + \frac{691878457}{8} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( 0\) , \( -25 a^{2} - 44 a + 56\) , \( 33 a^{2} + 58 a - 72\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-25a^{2}-44a+56\right){x}+33a^{2}+58a-72$ |
| 2.1-b1 |
2.1-b |
$2$ |
$7$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{14} \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \) |
$0.079681162$ |
$71.10047239$ |
0.969624222 |
\( -\frac{224839721}{16384} a^{2} + \frac{885052867}{16384} a - \frac{805139583}{16384} \) |
\( \bigl[a^{2} + a - 5\) , \( -a - 1\) , \( a^{2} - 4\) , \( -379 a^{2} - 666 a + 823\) , \( 10302 a^{2} + 18044 a - 22467\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-379a^{2}-666a+823\right){x}+10302a^{2}+18044a-22467$ |
| 2.1-b2 |
2.1-b |
$2$ |
$7$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \) |
$0.557768136$ |
$10.15721034$ |
0.969624222 |
\( \frac{69094930822433113167991627383}{4} a^{2} - \frac{10980381888813845455849280285}{4} a - \frac{492899924679101658545083410975}{4} \) |
\( \bigl[a^{2} + a - 5\) , \( -a - 1\) , \( a^{2} - 4\) , \( -16219 a^{2} - 28426 a + 35323\) , \( -3303424 a^{2} - 5786015 a + 7203555\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16219a^{2}-28426a+35323\right){x}-3303424a^{2}-5786015a+7203555$ |
| 2.1-c1 |
2.1-c |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$284.8336428$ |
2.031212457 |
\( \frac{4403272569}{16} a^{2} + \frac{7712719517}{16} a - \frac{9600947553}{16} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 4\) , \( a\) , \( -1324506 a^{2} - 2319915 a + 2888224\) , \( 1871200027 a^{2} + 3277466860 a - 4080345012\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-1324506a^{2}-2319915a+2888224\right){x}+1871200027a^{2}+3277466860a-4080345012$ |
| 2.1-c2 |
2.1-c |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$17.80210267$ |
2.031212457 |
\( \frac{2274554668646371}{2} a^{2} - \frac{8171598634156123}{2} a + \frac{5263924404422103}{2} \) |
\( \bigl[1\) , \( a^{2} + a - 4\) , \( 0\) , \( -8 a^{2} + 4 a + 64\) , \( 30 a^{2} + 13 a - 168\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-8a^{2}+4a+64\right){x}+30a^{2}+13a-168$ |
| 2.1-c3 |
2.1-c |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$142.4168214$ |
2.031212457 |
\( \frac{31509929}{4} a^{2} - \frac{113095007}{4} a + \frac{72840135}{4} \) |
\( \bigl[1\) , \( -a^{2} - a + 5\) , \( 1\) , \( -1250586149 a^{2} - 2190441747 a + 2727032325\) , \( 53511573663218 a^{2} + 93727237470105 a - 116687515765981\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-1250586149a^{2}-2190441747a+2727032325\right){x}+53511573663218a^{2}+93727237470105a-116687515765981$ |
| 2.1-c4 |
2.1-c |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$71.20841070$ |
2.031212457 |
\( -\frac{472343}{2} a^{2} + \frac{80155}{2} a + \frac{3360153}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a^{2} - 5\) , \( -1728747069475281463586 a^{2} - 3027955935779761443429 a + 3769711617796243640663\) , \( -44469415992243646591809768242552 a^{2} - 77889608313403371924358197009217 a + 96970156631101034810453944502741\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1728747069475281463586a^{2}-3027955935779761443429a+3769711617796243640663\right){x}-44469415992243646591809768242552a^{2}-77889608313403371924358197009217a+96970156631101034810453944502741$ |
| 2.1-d1 |
2.1-d |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.119646775$ |
$241.4818706$ |
1.236234470 |
\( \frac{4403272569}{16} a^{2} + \frac{7712719517}{16} a - \frac{9600947553}{16} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 5\) , \( a^{2} - 4\) , \( 53434 a^{2} - 8470 a - 381243\) , \( 12192335 a^{2} - 1937689 a - 86975689\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(53434a^{2}-8470a-381243\right){x}+12192335a^{2}-1937689a-86975689$ |
| 2.1-d2 |
2.1-d |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.239293551$ |
$482.9637412$ |
1.236234470 |
\( \frac{31509929}{4} a^{2} - \frac{113095007}{4} a + \frac{72840135}{4} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} + a - 4\) , \( 151 a^{2} - 23 a - 1079\) , \( -903 a^{2} + 141 a + 6437\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(151a^{2}-23a-1079\right){x}-903a^{2}+141a+6437$ |
| 2.1-d3 |
2.1-d |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.478587103$ |
$120.7409353$ |
1.236234470 |
\( \frac{2274554668646371}{2} a^{2} - \frac{8171598634156123}{2} a + \frac{5263924404422103}{2} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} + a - 4\) , \( -539 a^{2} + 102 a + 3801\) , \( -5903 a^{2} + 887 a + 42239\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-539a^{2}+102a+3801\right){x}-5903a^{2}+887a+42239$ |
| 2.1-d4 |
2.1-d |
$4$ |
$4$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.119646775$ |
$482.9637412$ |
1.236234470 |
\( -\frac{472343}{2} a^{2} + \frac{80155}{2} a + \frac{3360153}{2} \) |
\( \bigl[a + 1\) , \( -a^{2} + 5\) , \( a\) , \( a^{2} - a - 11\) , \( -a^{2} + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(a^{2}-a-11\right){x}-a^{2}+5$ |
| 2.1-e1 |
2.1-e |
$2$ |
$7$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 2 \) |
$1$ |
$0.272210257$ |
0.760947371 |
\( \frac{69094930822433113167991627383}{4} a^{2} - \frac{10980381888813845455849280285}{4} a - \frac{492899924679101658545083410975}{4} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + 5\) , \( a + 1\) , \( 475 a^{2} - 74 a - 3402\) , \( 11233 a^{2} - 775 a - 82929\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(475a^{2}-74a-3402\right){x}+11233a^{2}-775a-82929$ |
| 2.1-e2 |
2.1-e |
$2$ |
$7$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{14} \) |
$3.51630$ |
$(a^2+2a-2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$93.36811843$ |
0.760947371 |
\( -\frac{224839721}{16384} a^{2} + \frac{885052867}{16384} a - \frac{805139583}{16384} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + 5\) , \( a + 1\) , \( -5 a^{2} + 6 a + 18\) , \( 3 a^{2} - 16 a + 21\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-5a^{2}+6a+18\right){x}+3a^{2}-16a+21$ |
| 2.1-f1 |
2.1-f |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$0.215013826$ |
$147.5822901$ |
1.357737931 |
\( \frac{309494297}{64} a^{2} - \frac{1103588115}{64} a + \frac{709886159}{64} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a + 1\) , \( -3809 a^{2} + 13686 a - 8818\) , \( 390822 a^{2} - 1404071 a + 904456\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-3809a^{2}+13686a-8818\right){x}+390822a^{2}-1404071a+904456$ |
| 2.1-f2 |
2.1-f |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$3.51630$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$0.430027652$ |
$147.5822901$ |
1.357737931 |
\( -\frac{96991897}{8} a^{2} + \frac{15429267}{8} a + \frac{691878457}{8} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( -10 a^{2} + 41 a - 23\) , \( 66 a^{2} - 228 a + 143\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-10a^{2}+41a-23\right){x}+66a^{2}-228a+143$ |
| 4.2-a1 |
4.2-a |
$1$ |
$1$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$3.94692$ |
$(a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$35.78258618$ |
3.062083570 |
\( 137904 a^{2} - 21904 a - 983856 \) |
\( \bigl[0\) , \( a^{2} + a - 6\) , \( a^{2} - 4\) , \( 3 a^{2} - 19\) , \( a^{2} - 2 a - 14\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(3a^{2}-19\right){x}+a^{2}-2a-14$ |
| 4.2-b1 |
4.2-b |
$1$ |
$1$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$3.94692$ |
$(a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$76.83632828$ |
2.191748217 |
\( 137904 a^{2} - 21904 a - 983856 \) |
\( \bigl[0\) , \( a^{2} + a - 6\) , \( a^{2} - 4\) , \( -8 a^{2} + 29 a - 13\) , \( -133 a^{2} + 480 a - 314\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-8a^{2}+29a-13\right){x}-133a^{2}+480a-314$ |
| 6.1-a1 |
6.1-a |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$346.4727102$ |
2.470774443 |
\( \frac{43542577}{2304} a^{2} - \frac{192978715}{2304} a + \frac{227691959}{2304} \) |
\( \bigl[a^{2} - 5\) , \( 1\) , \( a + 1\) , \( -4328383 a^{2} + 15551022 a - 10019259\) , \( 14817330889 a^{2} - 53232972057 a + 34291273587\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-4328383a^{2}+15551022a-10019259\right){x}+14817330889a^{2}-53232972057a+34291273587$ |
| 6.1-a2 |
6.1-a |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{4} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$2.706818048$ |
2.470774443 |
\( \frac{9708664347469205}{162} a^{2} + \frac{17003358337492399}{162} a - \frac{21169333939648307}{162} \) |
\( \bigl[1\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( -2791490 a^{2} + 10028781 a - 6460333\) , \( -7689390681 a^{2} + 27625018439 a - 17795295307\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-2791490a^{2}+10028781a-6460333\right){x}-7689390681a^{2}+27625018439a-17795295307$ |
| 6.1-a3 |
6.1-a |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{8} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$21.65454438$ |
2.470774443 |
\( \frac{52394989985}{26244} a^{2} + \frac{112218557593}{26244} a - \frac{56271500177}{26244} \) |
\( \bigl[1\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( -174680 a^{2} + 627596 a - 404353\) , \( -119798471 a^{2} + 430389834 a - 277245745\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-174680a^{2}+627596a-404353\right){x}-119798471a^{2}+430389834a-277245745$ |
| 6.1-a4 |
6.1-a |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{16} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$2.706818048$ |
2.470774443 |
\( -\frac{107641112262050920517}{86093442} a^{2} + \frac{17106038037792641345}{86093442} a + \frac{767875377865994611619}{86093442} \) |
\( \bigl[1\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( -79870 a^{2} + 287531 a - 186453\) , \( -249156817 a^{2} + 895131405 a - 576634263\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-79870a^{2}+287531a-186453\right){x}-249156817a^{2}+895131405a-576634263$ |
| 6.1-a5 |
6.1-a |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$173.2363551$ |
2.470774443 |
\( \frac{349145}{1296} a^{2} + \frac{914845}{1296} a + \frac{2301727}{1296} \) |
\( \bigl[1\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( -17055 a^{2} + 61276 a - 39473\) , \( 473168 a^{2} - 1699910 a + 1095035\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-17055a^{2}+61276a-39473\right){x}+473168a^{2}-1699910a+1095035$ |
| 6.1-a6 |
6.1-a |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{2} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$86.61817755$ |
2.470774443 |
\( -\frac{1513}{36} a^{2} - \frac{8537}{36} a + \frac{49225}{36} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 195 a^{2} - 703 a + 452\) , \( 855 a^{2} - 3073 a + 1979\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(195a^{2}-703a+452\right){x}+855a^{2}-3073a+1979$ |
| 6.1-b1 |
6.1-b |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{16} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.315171813$ |
$24.76625556$ |
1.393664252 |
\( -\frac{107641112262050920517}{86093442} a^{2} + \frac{17106038037792641345}{86093442} a + \frac{767875377865994611619}{86093442} \) |
\( \bigl[a^{2} - 5\) , \( 1\) , \( 0\) , \( 4599 a^{2} - 727 a - 32816\) , \( -299090 a^{2} + 47492 a + 2133714\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+{x}^{2}+\left(4599a^{2}-727a-32816\right){x}-299090a^{2}+47492a+2133714$ |
| 6.1-b2 |
6.1-b |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{8} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.657585906$ |
$99.06502226$ |
1.393664252 |
\( \frac{52394989985}{26244} a^{2} + \frac{112218557593}{26244} a - \frac{56271500177}{26244} \) |
\( \bigl[a^{2} - 5\) , \( 1\) , \( 0\) , \( 284 a^{2} - 37 a - 2046\) , \( -4266 a^{2} + 663 a + 30474\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+{x}^{2}+\left(284a^{2}-37a-2046\right){x}-4266a^{2}+663a+30474$ |
| 6.1-b3 |
6.1-b |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{4} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.315171813$ |
$24.76625556$ |
1.393664252 |
\( \frac{9708664347469205}{162} a^{2} + \frac{17003358337492399}{162} a - \frac{21169333939648307}{162} \) |
\( \bigl[a^{2} - 5\) , \( 1\) , \( 0\) , \( 209 a^{2} + 93 a - 1836\) , \( -5406 a^{2} - 326 a + 41826\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+{x}^{2}+\left(209a^{2}+93a-1836\right){x}-5406a^{2}-326a+41826$ |
| 6.1-b4 |
6.1-b |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.328792953$ |
$198.1300445$ |
1.393664252 |
\( \frac{349145}{1296} a^{2} + \frac{914845}{1296} a + \frac{2301727}{1296} \) |
\( \bigl[a^{2} - 5\) , \( 1\) , \( 0\) , \( 19 a^{2} - 2 a - 136\) , \( -15 a^{2} + 3 a + 106\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+{x}^{2}+\left(19a^{2}-2a-136\right){x}-15a^{2}+3a+106$ |
| 6.1-b5 |
6.1-b |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{2} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.164396476$ |
$99.06502226$ |
1.393664252 |
\( -\frac{1513}{36} a^{2} - \frac{8537}{36} a + \frac{49225}{36} \) |
\( \bigl[1\) , \( a^{2} + a - 5\) , \( a^{2} - 4\) , \( 2 a + 4\) , \( a^{2} + a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(2a+4\right){x}+a^{2}+a-6$ |
| 6.1-b6 |
6.1-b |
$6$ |
$8$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$4.22286$ |
$(a^2+2a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.164396476$ |
$99.06502226$ |
1.393664252 |
\( \frac{43542577}{2304} a^{2} - \frac{192978715}{2304} a + \frac{227691959}{2304} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 6352 a^{2} - 815 a - 45847\) , \( 496533 a^{2} - 76208 a - 3549527\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6352a^{2}-815a-45847\right){x}+496533a^{2}-76208a-3549527$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{59} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 41 \) |
$1$ |
$3.465473455$ |
4.052942962 |
\( \frac{96398827169959}{2199023255552} a^{2} + \frac{230336111394003}{2199023255552} a - \frac{50786502856911}{2199023255552} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -3 a^{2} + 21\) , \( -888 a^{2} + 3265 a - 2261\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a^{2}+21\right){x}-888a^{2}+3265a-2261$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$37.54000213$ |
2.141649258 |
\( \frac{107232513023}{4} a^{2} - \frac{1540980409209}{16} a + \frac{496329141901}{8} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( -210 a^{2} + 805 a - 617\) , \( -5560 a^{2} + 19866 a - 12565\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-210a^{2}+805a-617\right){x}-5560a^{2}+19866a-12565$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{17} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$37.54000213$ |
2.141649258 |
\( -\frac{10037351}{256} a^{2} + \frac{8887209}{64} a - \frac{4932727}{64} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( 1\) , \( 4 a - 2\) , \( -a^{2} + 3 a - 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(4a-2\right){x}-a^{2}+3a-2$ |
| 8.1-c1 |
8.1-c |
$2$ |
$5$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$4.792270367$ |
0.683495051 |
\( -\frac{82580531100060065577}{32} a^{2} - \frac{36160612176795834363}{8} a + \frac{45018845293859152751}{8} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 4\) , \( a^{2} - 5\) , \( -101 a^{2} + 353 a - 210\) , \( 1775 a^{2} - 6805 a + 5284\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-101a^{2}+353a-210\right){x}+1775a^{2}-6805a+5284$ |
| 8.1-c2 |
8.1-c |
$2$ |
$5$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{7} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$23.96135183$ |
0.683495051 |
\( \frac{16359}{32} a^{2} - \frac{44157}{32} a - \frac{224431}{32} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 4\) , \( a^{2} - 5\) , \( -a^{2} - 2 a + 10\) , \( -6 a^{2} + 29 a - 36\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{2}-2a+10\right){x}-6a^{2}+29a-36$ |
| 8.1-d1 |
8.1-d |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{27} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$9.850623189$ |
0.842963984 |
\( \frac{3018045247}{4096} a^{2} + \frac{8635842411}{4096} a + \frac{1051581385}{2048} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( 1\) , \( 31 a^{2} - 236\) , \( 182 a^{2} + 548 a - 2886\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(31a^{2}-236\right){x}+182a^{2}+548a-2886$ |
| 8.1-d2 |
8.1-d |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$265.9668261$ |
0.842963984 |
\( -340 a^{2} + \frac{7833}{16} a + \frac{28441}{8} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( 1\) , \( -4 a^{2} + 29\) , \( 4 a^{2} - 22 a + 30\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-4a^{2}+29\right){x}+4a^{2}-22a+30$ |
| 8.1-d3 |
8.1-d |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$9.850623189$ |
0.842963984 |
\( \frac{443277743025019}{32} a^{2} + \frac{776415182867919}{32} a - \frac{1933225844567899}{64} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 6\) , \( a + 1\) , \( -2063 a^{2} + 13873 a - 22560\) , \( -357909 a^{2} + 1454075 a - 1291234\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-2063a^{2}+13873a-22560\right){x}-357909a^{2}+1454075a-1291234$ |
| 8.1-d4 |
8.1-d |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$265.9668261$ |
0.842963984 |
\( -1285529 a^{2} + \frac{825993}{4} a + \frac{36869243}{4} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 6\) , \( a + 1\) , \( 447 a^{2} + 1288 a - 6935\) , \( -10325 a^{2} - 40924 a + 190770\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(447a^{2}+1288a-6935\right){x}-10325a^{2}-40924a+190770$ |
| 8.1-e1 |
8.1-e |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$124.1303304$ |
1.770402338 |
\( -340 a^{2} + \frac{7833}{16} a + \frac{28441}{8} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( -5 a^{2} - 3 a + 28\) , \( -3 a^{2} + 2 a + 26\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-5a^{2}-3a+28\right){x}-3a^{2}+2a+26$ |
| 8.1-e2 |
8.1-e |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{27} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$41.37677682$ |
1.770402338 |
\( \frac{3018045247}{4096} a^{2} + \frac{8635842411}{4096} a + \frac{1051581385}{2048} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( -50 a^{2} - 83 a + 123\) , \( -356 a^{2} - 619 a + 789\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-50a^{2}-83a+123\right){x}-356a^{2}-619a+789$ |
| 8.1-e3 |
8.1-e |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$20.68838841$ |
1.770402338 |
\( \frac{443277743025019}{32} a^{2} + \frac{776415182867919}{32} a - \frac{1933225844567899}{64} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 6\) , \( 0\) , \( 22 a^{2} + 27 a - 234\) , \( 20 a^{2} - 171 a + 322\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(22a^{2}+27a-234\right){x}+20a^{2}-171a+322$ |
| 8.1-e4 |
8.1-e |
$4$ |
$6$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$62.06516523$ |
1.770402338 |
\( -1285529 a^{2} + \frac{825993}{4} a + \frac{36869243}{4} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 6\) , \( 0\) , \( 12 a^{2} + 2 a - 89\) , \( 86 a^{2} - 11 a - 617\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(12a^{2}+2a-89\right){x}+86a^{2}-11a-617$ |
| 8.1-f1 |
8.1-f |
$2$ |
$5$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{7} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$116.9388896$ |
0.667133916 |
\( \frac{16359}{32} a^{2} - \frac{44157}{32} a - \frac{224431}{32} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 4\) , \( -3 a^{2} - 2 a + 15\) , \( -3 a^{2} - 2 a + 15\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-3a^{2}-2a+15\right){x}-3a^{2}-2a+15$ |
| 8.1-f2 |
8.1-f |
$2$ |
$5$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.935511117$ |
0.667133916 |
\( -\frac{82580531100060065577}{32} a^{2} - \frac{36160612176795834363}{8} a + \frac{45018845293859152751}{8} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 4\) , \( -783 a^{2} - 1367 a + 1715\) , \( -25629 a^{2} - 44886 a + 55893\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-783a^{2}-1367a+1715\right){x}-25629a^{2}-44886a+55893$ |
| 8.1-g1 |
8.1-g |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{17} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$238.7350751$ |
3.404946507 |
\( -\frac{10037351}{256} a^{2} + \frac{8887209}{64} a - \frac{4932727}{64} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 5\) , \( a^{2} - 5\) , \( -767 a^{2} - 1350 a + 1654\) , \( 21622 a^{2} + 37875 a - 47141\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-767a^{2}-1350a+1654\right){x}+21622a^{2}+37875a-47141$ |
| 8.1-g2 |
8.1-g |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$119.3675375$ |
3.404946507 |
\( \frac{107232513023}{4} a^{2} - \frac{1540980409209}{16} a + \frac{496329141901}{8} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a + 1\) , \( 343 a^{2} - 54 a - 2445\) , \( 4801 a^{2} - 763 a - 34249\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(343a^{2}-54a-2445\right){x}+4801a^{2}-763a-34249$ |
| 8.1-h1 |
8.1-h |
$1$ |
$1$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{59} \) |
$4.43026$ |
$(a^2+2a-2), (-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3^{2} \) |
$1$ |
$8.960634523$ |
2.300410451 |
\( \frac{96398827169959}{2199023255552} a^{2} + \frac{230336111394003}{2199023255552} a - \frac{50786502856911}{2199023255552} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 5\) , \( 0\) , \( 377 a^{2} + 662 a - 817\) , \( 12205 a^{2} + 21378 a - 26611\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(377a^{2}+662a-817\right){x}+12205a^{2}+21378a-26611$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$4.43026$ |
$(a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$44.81966986$ |
2.556952777 |
\( -92740 a^{2} - 163604 a + 200356 \) |
\( \bigl[0\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( -1896 a^{2} - 3322 a + 4141\) , \( -101083 a^{2} - 177048 a + 220420\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-1896a^{2}-3322a+4141\right){x}-101083a^{2}-177048a+220420$ |
| 8.2-b1 |
8.2-b |
$2$ |
$2$ |
3.3.1229.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{11} \) |
$4.43026$ |
$(a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.371235766$ |
$248.1316736$ |
1.970685579 |
\( 14551 a^{2} + 36746 a - 2026 \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 6\) , \( a\) , \( -a^{2} - 2 a + 9\) , \( -a + 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-a^{2}-2a+9\right){x}-a+1$ |
*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.
