Atkin-Lehner |
3- 5+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825bl |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-24061417227421875 = -1 · 39 · 57 · 77 · 19 |
Discriminant |
Eigenvalues |
0 3- 5+ 7- 0 -4 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,59617,-4910356] |
[a1,a2,a3,a4,a6] |
Generators |
[268:-5513:1] |
Generators of the group modulo torsion |
j |
12747309056/13089195 |
j-invariant |
L |
5.9419289050139 |
L(r)(E,1)/r! |
Ω |
0.20565927199369 |
Real period |
R |
0.40127921074052 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000039 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13965g1 9975c1 |
Quadratic twists by: 5 -7 |