| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 4.2-a1 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$973.0976459$ |
0.635703654 |
\( -\frac{1461523}{8} a^{3} + \frac{2301089}{16} a^{2} + 1087849 a + \frac{2377973}{4} \) |
\( \bigl[a^{2} - a - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 2\) , \( -a^{3} - a^{2} + a + 3\) , \( -9 a^{3} - 10 a^{2} + 17 a + 12\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-3\right){x}^{2}+\left(-a^{3}-a^{2}+a+3\right){x}-9a^{3}-10a^{2}+17a+12$ |
| 4.2-a2 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2 \) |
$1$ |
$3.003387796$ |
0.635703654 |
\( -\frac{29653231610314386102071328047}{8} a^{3} + \frac{23064539310446827140105105381}{8} a^{2} + \frac{176455439061398162337288952867}{8} a + \frac{97049389222729473531995752583}{8} \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( 0\) , \( 389 a^{3} - 299 a^{2} - 2314 a - 1313\) , \( 10214 a^{3} - 7910 a^{2} - 60808 a - 33659\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(389a^{3}-299a^{2}-2314a-1313\right){x}+10214a^{3}-7910a^{2}-60808a-33659$ |
| 4.2-a3 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$24.02710236$ |
0.635703654 |
\( -\frac{309879255131593}{16} a^{3} + \frac{964107191237127}{64} a^{2} + \frac{3687953989619557}{32} a + \frac{4056703310603201}{64} \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( 0\) , \( 19 a^{3} - 9 a^{2} - 114 a - 113\) , \( 180 a^{3} - 116 a^{2} - 1088 a - 763\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(19a^{3}-9a^{2}-114a-113\right){x}+180a^{3}-116a^{2}-1088a-763$ |
| 4.2-a4 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$243.2744114$ |
0.635703654 |
\( 6838817718264 a^{3} + 7293784227856 a^{2} - \frac{23657289875359}{2} a - \frac{17840410458761}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( 0\) , \( 4 a^{3} - 4 a^{2} - 24 a - 8\) , \( 23 a^{3} - 19 a^{2} - 134 a - 66\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(4a^{3}-4a^{2}-24a-8\right){x}+23a^{3}-19a^{2}-134a-66$ |
| 4.2-a5 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1946.195291$ |
0.635703654 |
\( 455112 a^{3} + \frac{1978081}{4} a^{2} - \frac{1527673}{2} a - \frac{2310543}{4} \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( 0\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(-a^{3}+a^{2}+6a+2\right){x}$ |
| 4.2-a6 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2 \) |
$1$ |
$3.003387796$ |
0.635703654 |
\( -\frac{22147283405268829150571394397}{8} a^{3} + \frac{80536490720719603365180339507}{8} a^{2} - \frac{21053894014648516579360785535}{8} a - \frac{27068218753999011991096133191}{4} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{117}{2} a^{3} - 9 a^{2} + \frac{327}{2} a - 77\) , \( -909 a^{3} - 1518 a^{2} + 1521 a + 2068\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-\frac{117}{2}a^{3}-9a^{2}+\frac{327}{2}a-77\right){x}-909a^{3}-1518a^{2}+1521a+2068$ |
| 4.2-a7 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$24.02710236$ |
0.635703654 |
\( -\frac{462882705755995}{32} a^{3} + \frac{3366457672839597}{64} a^{2} - \frac{220015170781007}{16} a - \frac{565731125604339}{16} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{107}{2} a^{3} - 49 a^{2} + \frac{197}{2} a + 53\) , \( -740 a^{3} - 770 a^{2} + 1292 a + 922\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-\frac{107}{2}a^{3}-49a^{2}+\frac{197}{2}a+53\right){x}-740a^{3}-770a^{2}+1292a+922$ |
| 4.2-a8 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1946.195291$ |
0.635703654 |
\( 2160606 a^{3} - \frac{22903825}{4} a^{2} - \frac{14166635}{2} a + \frac{26536123}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 4\) , \( a\) , \( a^{3} - a^{2} + a + 6\) , \( a^{3} + a^{2} - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-4\right){x}^{2}+\left(a^{3}-a^{2}+a+6\right){x}+a^{3}+a^{2}-2$ |
| 4.2-a9 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$243.2744114$ |
0.635703654 |
\( \frac{128616565964817}{4} a^{3} - \frac{170559405293585}{2} a^{2} - \frac{420600930762901}{4} a + \frac{394396376368601}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 4\) , \( a\) , \( \frac{7}{2} a^{3} - 11 a^{2} + \frac{17}{2} a + 11\) , \( \frac{27}{2} a^{3} - 41 a^{2} + \frac{15}{2} a + 35\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-4\right){x}^{2}+\left(\frac{7}{2}a^{3}-11a^{2}+\frac{17}{2}a+11\right){x}+\frac{27}{2}a^{3}-41a^{2}+\frac{15}{2}a+35$ |
| 4.2-a10 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$973.0976459$ |
0.635703654 |
\( -\frac{1074913}{8} a^{3} + \frac{7844655}{16} a^{2} - \frac{273371}{2} a - \frac{5120243}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - 2 a^{2} - \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 1\) , \( -8 a^{3} + 20 a^{2} + 28 a - 42\) , \( -30 a^{3} + 79 a^{2} + 99 a - 180\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(-8a^{3}+20a^{2}+28a-42\right){x}-30a^{3}+79a^{2}+99a-180$ |
| 4.2-a11 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{27} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$12.01355118$ |
0.635703654 |
\( \frac{858977541416295}{2048} a^{3} - \frac{4556389024089385}{4096} a^{2} - \frac{351125163504689}{256} a + \frac{10535946209653885}{4096} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( \frac{45}{2} a^{3} + 20 a^{2} - \frac{67}{2} a - 28\) , \( -92 a^{3} - 109 a^{2} + 166 a + 127\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(\frac{45}{2}a^{3}+20a^{2}-\frac{67}{2}a-28\right){x}-92a^{3}-109a^{2}+166a+127$ |
| 4.2-a12 |
4.2-a |
$12$ |
$24$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{27} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$12.01355118$ |
0.635703654 |
\( \frac{182703770309879}{2048} a^{3} + \frac{389663777184689}{4096} a^{2} - \frac{158021313570505}{1024} a - \frac{119159562829617}{1024} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( a - 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( \frac{133}{2} a^{3} - 64 a^{2} - \frac{747}{2} a - 177\) , \( 463 a^{3} - 364 a^{2} - 2745 a - 1528\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{133}{2}a^{3}-64a^{2}-\frac{747}{2}a-177\right){x}+463a^{3}-364a^{2}-2745a-1528$ |
| 4.2-b1 |
4.2-b |
$4$ |
$22$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 11$ |
2B, 11B.1.2 |
$14641$ |
\( 2 \) |
$1$ |
$0.028936025$ |
2.490866296 |
\( -\frac{77104951652875056890756025}{4} a^{3} + \frac{29986448219866606484242417}{2} a^{2} + \frac{458823115018563237137028205}{4} a + \frac{126174923568896740874837415}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -3195 a^{3} - 3644 a^{2} + 4925 a + 2649\) , \( -429163 a^{3} - 463940 a^{2} + 727927 a + 537297\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3195a^{3}-3644a^{2}+4925a+2649\right){x}-429163a^{3}-463940a^{2}+727927a+537297$ |
| 4.2-b2 |
4.2-b |
$4$ |
$22$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{33} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/22\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 11$ |
2B, 11B.1.1 |
$1$ |
\( 2 \cdot 11^{2} \) |
$1$ |
$423.6523509$ |
2.490866296 |
\( \frac{2296475}{512} a^{3} + \frac{11641725}{2048} a^{2} - \frac{3623639}{512} a - \frac{2976765}{512} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{5}{2} a^{3} - 4 a^{2} + \frac{5}{2} a + 4\) , \( \frac{13}{2} a^{3} + 6 a^{2} - \frac{25}{2} a - 8\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-\frac{5}{2}a^{3}-4a^{2}+\frac{5}{2}a+4\right){x}+\frac{13}{2}a^{3}+6a^{2}-\frac{25}{2}a-8$ |
| 4.2-b3 |
4.2-b |
$4$ |
$22$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{33} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/22\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 11$ |
2B, 11B.1.1 |
$1$ |
\( 2 \cdot 11^{2} \) |
$1$ |
$423.6523509$ |
2.490866296 |
\( \frac{45730997}{2048} a^{3} - \frac{121475519}{2048} a^{2} - \frac{150256135}{2048} a + \frac{284340953}{2048} \) |
\( \bigl[a^{2} - a - 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( a^{2} - 2\) , \( -\frac{5}{2} a^{3} + \frac{37}{2} a + 7\) , \( a^{3} - a^{2} - 9 a - 4\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-3\right){x}^{2}+\left(-\frac{5}{2}a^{3}+\frac{37}{2}a+7\right){x}+a^{3}-a^{2}-9a-4$ |
| 4.2-b4 |
4.2-b |
$4$ |
$22$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{3} \) |
$9.03702$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 11$ |
2B, 11B.1.2 |
$14641$ |
\( 2 \) |
$1$ |
$0.028936025$ |
2.490866296 |
\( -14396957122230731117850794 a^{3} + 52353165960965687438958392 a^{2} - \frac{27372387296584646525275301}{2} a - \frac{70383347268241246319024927}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -15562 a^{3} + 41154 a^{2} + 51350 a - 96969\) , \( -\frac{3996567}{2} a^{3} + 5297744 a^{2} + \frac{13088811}{2} a - 12282560\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+1\right){x}^{2}+\left(-15562a^{3}+41154a^{2}+51350a-96969\right){x}-\frac{3996567}{2}a^{3}+5297744a^{2}+\frac{13088811}{2}a-12282560$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$171.2866744$ |
2.014161864 |
\( \frac{551595651}{2} a^{3} - \frac{1464255405}{2} a^{2} - 900972384 a + 1694698178 \) |
\( \bigl[a^{2} - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( a\) , \( -8 a^{3} - 7 a^{2} + 13 a + 9\) , \( -\frac{21}{2} a^{3} - 12 a^{2} + \frac{37}{2} a + 14\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}^{2}+\left(-8a^{3}-7a^{2}+13a+9\right){x}-\frac{21}{2}a^{3}-12a^{2}+\frac{37}{2}a+14$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$685.1466979$ |
2.014161864 |
\( -\frac{3981}{2} a^{3} + \frac{26961}{4} a^{2} - 1039 a - 4097 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 5\) , \( a\) , \( \frac{15}{2} a^{3} - a^{2} - \frac{29}{2} a + 7\) , \( -60 a^{3} + 214 a^{2} + 218 a - 477\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-5\right){x}^{2}+\left(\frac{15}{2}a^{3}-a^{2}-\frac{29}{2}a+7\right){x}-60a^{3}+214a^{2}+218a-477$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1370.293395$ |
2.014161864 |
\( 123401 a^{3} + \frac{218605}{2} a^{2} - 222930 a - 113386 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{7}{2} a - 5\) , \( a^{2} + 2 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{7}{2}a-5\right){x}+a^{2}+2a-6$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$685.1466979$ |
2.014161864 |
\( \frac{889860112433}{2} a^{3} + \frac{948983857013}{2} a^{2} - 769659297866 a - 580388944978 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( 2 a^{3} - 18 a^{2} + 16 a + 5\) , \( 27 a^{3} - 91 a^{2} + 16 a + 65\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{3}-18a^{2}+16a+5\right){x}+27a^{3}-91a^{2}+16a+65$ |
| 8.2-a1 |
8.2-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{9} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$685.1466979$ |
2.014161864 |
\( \frac{8367390130191}{4} a^{3} - 5548047106035 a^{2} - \frac{27362693873707}{4} a + \frac{25658082330089}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( a + 1\) , \( \frac{551}{2} a^{3} - 213 a^{2} - \frac{3273}{2} a - 902\) , \( \frac{12291}{2} a^{3} - 4778 a^{2} - \frac{73129}{2} a - 20110\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(\frac{551}{2}a^{3}-213a^{2}-\frac{3273}{2}a-902\right){x}+\frac{12291}{2}a^{3}-4778a^{2}-\frac{73129}{2}a-20110$ |
| 8.2-a2 |
8.2-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{6} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1370.293395$ |
2.014161864 |
\( 553142 a^{3} - \frac{2924777}{2} a^{2} - 1806699 a + \frac{6772201}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( a + 1\) , \( 18 a^{3} - 13 a^{2} - 104 a - 57\) , \( \frac{219}{2} a^{3} - 83 a^{2} - \frac{1293}{2} a - 356\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(18a^{3}-13a^{2}-104a-57\right){x}+\frac{219}{2}a^{3}-83a^{2}-\frac{1293}{2}a-356$ |
| 8.2-a3 |
8.2-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{12} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$685.1466979$ |
2.014161864 |
\( -\frac{5473}{2} a^{3} + \frac{10855}{4} a^{2} + 15220 a + \frac{26861}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -a^{2} + a + 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 2\) , \( a^{3} + 3\) , \( -13 a^{3} - 14 a^{2} + 23 a + 17\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(a^{3}+3\right){x}-13a^{3}-14a^{2}+23a+17$ |
| 8.2-a4 |
8.2-a |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{9} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$171.2866744$ |
2.014161864 |
\( \frac{233905281}{4} a^{3} + 63579411 a^{2} - \frac{407400213}{4} a - \frac{154496201}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( 0\) , \( -3 a^{3} + 3 a^{2} + 25 a + 4\) , \( \frac{27}{2} a^{3} - 19 a^{2} - \frac{113}{2} a - 17\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-3\right){x}^{2}+\left(-3a^{3}+3a^{2}+25a+4\right){x}+\frac{27}{2}a^{3}-19a^{2}-\frac{113}{2}a-17$ |
| 8.3-a1 |
8.3-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$957.9492177$ |
1.408066906 |
\( -11118 a^{3} + 40563 a^{2} - 9672 a - 24898 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 5\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 1\) , \( \frac{13}{2} a^{3} - \frac{25}{2} a + 2\) , \( 7 a^{3} + 8 a^{2} - 10 a - 13\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-5\right){x}^{2}+\left(\frac{13}{2}a^{3}-\frac{25}{2}a+2\right){x}+7a^{3}+8a^{2}-10a-13$ |
| 8.3-a2 |
8.3-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{4} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$239.4873044$ |
1.408066906 |
\( -45989313 a^{3} + 35771294 a^{2} + 273664524 a + 150513352 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( a^{2} - 2 a - 4\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 1\) , \( 2 a^{3} + 7 a^{2} - a - 10\) , \( \frac{7}{2} a^{3} + 19 a^{2} - \frac{1}{2} a - 36\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(2a^{3}+7a^{2}-a-10\right){x}+\frac{7}{2}a^{3}+19a^{2}-\frac{1}{2}a-36$ |
| 8.3-a3 |
8.3-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{11} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$119.7436522$ |
1.408066906 |
\( -\frac{3289415699}{2} a^{3} + 5983043609 a^{2} - \frac{3121446849}{2} a - 4019420473 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( a - 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( 35 a^{3} - 60 a^{2} - 132 a + 75\) , \( -47 a^{3} + 86 a^{2} + 289 a + 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(35a^{3}-60a^{2}-132a+75\right){x}-47a^{3}+86a^{2}+289a+9$ |
| 8.3-a4 |
8.3-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{10} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$239.4873044$ |
1.408066906 |
\( 25697255441 a^{3} - 68144234508 a^{2} - 84029931624 a + 157577020102 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( -\frac{13}{2} a^{3} + 16 a^{2} + \frac{39}{2} a - 35\) , \( -11 a^{3} + 30 a^{2} + 36 a - 69\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{13}{2}a^{3}+16a^{2}+\frac{39}{2}a-35\right){x}-11a^{3}+30a^{2}+36a-69$ |
| 8.3-a5 |
8.3-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$957.9492177$ |
1.408066906 |
\( 59260 a^{3} - 160031 a^{2} - 187884 a + 382560 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( -\frac{3}{2} a^{3} + 6 a^{2} - \frac{1}{2} a - 5\) , \( -a^{3} + 4 a^{2} - a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{3}{2}a^{3}+6a^{2}-\frac{1}{2}a-5\right){x}-a^{3}+4a^{2}-a-3$ |
| 8.3-a6 |
8.3-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{11} \) |
$9.85494$ |
$(-1/2a^3+a^2+5/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$478.9746088$ |
1.408066906 |
\( \frac{57831}{2} a^{3} - 76797 a^{2} - \frac{188655}{2} a + 177977 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( a^{2} - a - 2\) , \( -a^{3} + 4 a^{2} + 5 a - 2\) , \( 2 a^{3} - a^{2} - 6 a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}^{2}+\left(-a^{3}+4a^{2}+5a-2\right){x}+2a^{3}-a^{2}-6a$ |
| 8.4-a1 |
8.4-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$9.85494$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$239.4873044$ |
1.408066906 |
\( \frac{10956898329}{2} a^{3} + 5792825297 a^{2} - \frac{18994364385}{2} a - 7046823134 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( a + 1\) , \( \frac{115}{2} a^{3} - 34 a^{2} - \frac{641}{2} a - 179\) , \( -440 a^{3} + 367 a^{2} + 2694 a + 1479\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}^{2}+\left(\frac{115}{2}a^{3}-34a^{2}-\frac{641}{2}a-179\right){x}-440a^{3}+367a^{2}+2694a+1479$ |
| 8.4-a2 |
8.4-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$9.85494$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$957.9492177$ |
1.408066906 |
\( -14304 a^{3} + 10281 a^{2} + 85938 a + 53993 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -a^{2} + a + 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 1\) , \( -2 a^{3} + 10 a^{2} + 9 a - 22\) , \( -6 a^{3} + 25 a^{2} + 20 a - 61\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{3}+10a^{2}+9a-22\right){x}-6a^{3}+25a^{2}+20a-61$ |
| 8.4-a3 |
8.4-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$9.85494$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$239.4873044$ |
1.408066906 |
\( -\frac{68696705}{2} a^{3} + 124904037 a^{2} - \frac{65303055}{2} a - 83959466 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a + 3\) , \( a + 1\) , \( -\frac{3}{2} a^{3} + a^{2} + \frac{17}{2} a + 7\) , \( -2 a^{3} - a^{2} + 7 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{3}{2}a^{3}+a^{2}+\frac{17}{2}a+7\right){x}-2a^{3}-a^{2}+7a+5$ |
| 8.4-a4 |
8.4-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{11} \) |
$9.85494$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$478.9746088$ |
1.408066906 |
\( 6159 a^{3} + 6648 a^{2} - 10896 a - 7879 \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 2\) , \( a + 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} + 2 a^{2} - \frac{3}{2} a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-\frac{1}{2}a^{3}+2a^{2}-\frac{3}{2}a-2\right){x}-\frac{1}{2}a^{3}+2a^{2}-\frac{3}{2}a-2$ |
| 8.4-a5 |
8.4-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$9.85494$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$957.9492177$ |
1.408066906 |
\( 12697 a^{3} + 16117 a^{2} - 27987 a - 11247 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a + 1\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(\frac{1}{2}a^{3}+a^{2}-\frac{5}{2}a-3\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a$ |
| 8.4-a6 |
8.4-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{11} \) |
$9.85494$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$119.7436522$ |
1.408066906 |
\( -2198503426 a^{3} + 1703378942 a^{2} + 13090357251 a + 7233536771 \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a + 1\) , \( 132 a^{3} + 138 a^{2} - 228 a - 167\) , \( -431 a^{3} - 460 a^{2} + 745 a + 563\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(132a^{3}+138a^{2}-228a-167\right){x}-431a^{3}-460a^{2}+745a+563$ |
| 16.2-a1 |
16.2-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{4} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.841658498$ |
$155.4672309$ |
1.538670287 |
\( -45989313 a^{3} + 35771294 a^{2} + 273664524 a + 150513352 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} - \frac{1}{2} a - 4\) , \( 0\) , \( \frac{19}{2} a^{3} - \frac{89}{2} a - 24\) , \( \frac{45}{2} a^{3} - 3 a^{2} - \frac{211}{2} a - 62\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}-\frac{1}{2}a-4\right){x}^{2}+\left(\frac{19}{2}a^{3}-\frac{89}{2}a-24\right){x}+\frac{45}{2}a^{3}-3a^{2}-\frac{211}{2}a-62$ |
| 16.2-a2 |
16.2-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{11} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.105207312$ |
$1243.737847$ |
1.538670287 |
\( \frac{57831}{2} a^{3} - 76797 a^{2} - \frac{188655}{2} a + 177977 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( a^{3} + 3 a^{2} + 3 a + 1\) , \( \frac{23}{2} a^{3} + 15 a^{2} - \frac{27}{2} a - 12\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(a^{3}+3a^{2}+3a+1\right){x}+\frac{23}{2}a^{3}+15a^{2}-\frac{27}{2}a-12$ |
| 16.2-a3 |
16.2-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{11} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.105207312$ |
$1243.737847$ |
1.538670287 |
\( -\frac{3289415699}{2} a^{3} + 5983043609 a^{2} - \frac{3121446849}{2} a - 4019420473 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a\) , \( a^{2} - 2\) , \( 15 a^{3} - 14 a^{2} - 101 a - 54\) , \( -73 a^{3} + 61 a^{2} + 440 a + 240\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a\right){x}^{2}+\left(15a^{3}-14a^{2}-101a-54\right){x}-73a^{3}+61a^{2}+440a+240$ |
| 16.2-a4 |
16.2-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.210414624$ |
$2487.475695$ |
1.538670287 |
\( -11118 a^{3} + 40563 a^{2} - 9672 a - 24898 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a\) , \( a^{2} - 2\) , \( a^{2} - 6 a - 4\) , \( -a^{3} + a^{2} + 2 a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a\right){x}^{2}+\left(a^{2}-6a-4\right){x}-a^{3}+a^{2}+2a$ |
| 16.2-a5 |
16.2-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.420829249$ |
$621.8689239$ |
1.538670287 |
\( 59260 a^{3} - 160031 a^{2} - 187884 a + 382560 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - 2 a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( 107 a^{3} - 85 a^{2} - 636 a - 343\) , \( \frac{2723}{2} a^{3} - 1060 a^{2} - \frac{16203}{2} a - 4453\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(107a^{3}-85a^{2}-636a-343\right){x}+\frac{2723}{2}a^{3}-1060a^{2}-\frac{16203}{2}a-4453$ |
| 16.2-a6 |
16.2-a |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.841658498$ |
$38.86680774$ |
1.538670287 |
\( 25697255441 a^{3} - 68144234508 a^{2} - 84029931624 a + 157577020102 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - 2 a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -58 a^{3} + 45 a^{2} + 344 a + 187\) , \( \frac{9623}{2} a^{3} - 3738 a^{2} - \frac{57277}{2} a - 15773\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-58a^{3}+45a^{2}+344a+187\right){x}+\frac{9623}{2}a^{3}-3738a^{2}-\frac{57277}{2}a-15773$ |
| 16.3-a1 |
16.3-a |
$2$ |
$2$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{11} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$404.4360997$ |
2.377884243 |
\( -\frac{86747}{2} a^{3} + \frac{315723}{2} a^{2} - 42626 a - 103044 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{1}{2} a - 3\) , \( 0\) , \( -\frac{17}{2} a^{3} + 42 a^{2} + \frac{69}{2} a - 89\) , \( 61 a^{3} - 114 a^{2} - 180 a + 279\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{17}{2}a^{3}+42a^{2}+\frac{69}{2}a-89\right){x}+61a^{3}-114a^{2}-180a+279$ |
| 16.3-a2 |
16.3-a |
$2$ |
$2$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{13} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$404.4360997$ |
2.377884243 |
\( \frac{2993}{2} a^{3} + \frac{3041}{2} a^{2} - \frac{3665}{2} a - 753 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( a^{3} - 4 a + 3\) , \( \frac{1}{2} a^{3} + 2 a^{2} - \frac{3}{2} a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(a^{3}-4a+3\right){x}+\frac{1}{2}a^{3}+2a^{2}-\frac{3}{2}a-3$ |
| 16.3-b1 |
16.3-b |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{15} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$157.2675851$ |
0.924655620 |
\( 837213 a^{3} + \frac{3585429}{4} a^{2} - \frac{2883847}{2} a - 1089460 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( 0\) , \( \frac{1}{2} a^{3} + 8 a^{2} - \frac{1}{2} a - 3\) , \( 4 a^{3} + a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+1\right){x}^{2}+\left(\frac{1}{2}a^{3}+8a^{2}-\frac{1}{2}a-3\right){x}+4a^{3}+a^{2}-2a-1$ |
| 16.3-b2 |
16.3-b |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$78.63379256$ |
0.924655620 |
\( -4947416289918956 a^{3} + \frac{7696286125260707}{2} a^{2} + \frac{58880497419321213}{2} a + 16191952886399857 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -3 a^{3} + 5 a^{2} + 40 a - 55\) , \( \frac{119}{2} a^{3} - 186 a^{2} - \frac{103}{2} a + 231\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}^{2}+\left(-3a^{3}+5a^{2}+40a-55\right){x}+\frac{119}{2}a^{3}-186a^{2}-\frac{103}{2}a+231$ |
| 16.3-b3 |
16.3-b |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$314.5351702$ |
0.924655620 |
\( -22371908 a^{3} + \frac{34790409}{2} a^{2} + 133136252 a + 73251608 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -3 a^{3} + 10 a^{2} + 15 a - 25\) , \( -\frac{15}{2} a^{3} + 24 a^{2} + \frac{59}{2} a - 59\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}^{2}+\left(-3a^{3}+10a^{2}+15a-25\right){x}-\frac{15}{2}a^{3}+24a^{2}+\frac{59}{2}a-59$ |
| 16.3-b4 |
16.3-b |
$4$ |
$4$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{9} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$157.2675851$ |
0.924655620 |
\( \frac{158335903}{2} a^{3} - \frac{419893619}{2} a^{2} - 258987932 a + 485594082 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 1\) , \( 28 a^{3} + 28 a^{2} - 56 a - 41\) , \( -553 a^{3} - 593 a^{2} + 947 a + 716\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{1}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}-a{x}^{2}+\left(28a^{3}+28a^{2}-56a-41\right){x}-553a^{3}-593a^{2}+947a+716$ |
| 16.3-c1 |
16.3-c |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{9} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.132393674$ |
$569.2689706$ |
1.772497108 |
\( \frac{135877313}{2} a^{3} + \frac{139135573}{2} a^{2} - 118616824 a - 82712306 \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( a^{2} - 2\) , \( -6 a^{3} + 24 a^{2} + 26 a - 56\) , \( -24 a^{3} + 86 a^{2} + 84 a - 188\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a^{3}+24a^{2}+26a-56\right){x}-24a^{3}+86a^{2}+84a-188$ |
| 16.3-c2 |
16.3-c |
$6$ |
$8$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{6} \) |
$10.74689$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.066196837$ |
$2277.075882$ |
1.772497108 |
\( -47123809 a^{3} + \frac{342736201}{2} a^{2} - 44802018 a - 115191426 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{41}{2} a^{3} - 5 a^{2} - \frac{195}{2} a - 55\) , \( 26 a^{3} + 14 a^{2} - 76 a - 48\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(\frac{41}{2}a^{3}-5a^{2}-\frac{195}{2}a-55\right){x}+26a^{3}+14a^{2}-76a-48$ |
*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.
