Atkin-Lehner |
2- 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
72128bi |
Isogeny class |
Conductor |
72128 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-89536051189645312 = -1 · 222 · 79 · 232 |
Discriminant |
Eigenvalues |
2- 2 2 7- 0 0 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-672737,213092993] |
[a1,a2,a3,a4,a6] |
Generators |
[-74009:33730620:2197] |
Generators of the group modulo torsion |
j |
-3183010111/8464 |
j-invariant |
L |
11.072474878982 |
L(r)(E,1)/r! |
Ω |
0.34059395747458 |
Real period |
R |
8.1273277436964 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993747 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72128v1 18032v1 72128bo1 |
Quadratic twists by: -4 8 -7 |