Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
47424a |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9698304 |
Modular degree for the optimal curve |
Δ |
2.3944437820617E+21 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 0 13+ -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1589570048,-24392605066614] |
[a1,a2,a3,a4,a6] |
Generators |
[1939650069507800107174106039785301934567031962203351468331220894207707547423836160692301229235998715833553216648262700201321046764756791010613046537339834475670291999525304523949689448273989174233026642318711218484927422793155902996166341727494215497045584590:-129487469001040742461697965022864725600563227711566819088776307048012895461194439120289086458871894898113056472561639580409502842424926925751565879946482615801932812186476903168838307950212112856262310677085455687710421970181723903400970265965568244589836983251:40345904238705448933180119650409006557014059476322620715170365125863851066704931222976584581578343867725327566952117797378936077772941553266959325796059332868216745788102425213955326076326432127091254246712011879951013677586697471005527356086070045679000] |
Generators of the group modulo torsion |
j |
6940372030738141738872723112000/37413184094713647207 |
j-invariant |
L |
4.7876320059988 |
L(r)(E,1)/r! |
Ω |
0.023910003356681 |
Real period |
R |
400.47104423856 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47424be1 23712r2 |
Quadratic twists by: -4 8 |