Atkin-Lehner |
3- 5- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
68355v |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
483840 |
Modular degree for the optimal curve |
Δ |
87938148014325 = 39 · 52 · 78 · 31 |
Discriminant |
Eigenvalues |
-2 3- 5- 7+ -1 -2 -5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-167727,26435610] |
[a1,a2,a3,a4,a6] |
Generators |
[98:-3308:1] [-52:5917:1] |
Generators of the group modulo torsion |
j |
124171177984/20925 |
j-invariant |
L |
5.8517372243432 |
L(r)(E,1)/r! |
Ω |
0.58558425331065 |
Real period |
R |
0.4163745574997 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998613 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22785k1 68355p1 |
Quadratic twists by: -3 -7 |