Atkin-Lehner |
2- 3+ 29+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
84912o |
Isogeny class |
Conductor |
84912 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
628992 |
Modular degree for the optimal curve |
Δ |
-2904821858304 = -1 · 221 · 33 · 292 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 3 -2 -6 2 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-631824,-193094208] |
[a1,a2,a3,a4,a6] |
Generators |
[3426488:112299136:2197] |
Generators of the group modulo torsion |
j |
-6810089311480188817/709185024 |
j-invariant |
L |
5.4935054803176 |
L(r)(E,1)/r! |
Ω |
0.08466822775145 |
Real period |
R |
8.1103408331074 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003499 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10614q1 |
Quadratic twists by: -4 |