Atkin-Lehner |
2+ 3+ 7- 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544x |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-3456057024 = -1 · 26 · 33 · 76 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7- -5 7 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3666,85482] |
[a1,a2,a3,a4,a6] |
Generators |
[33:21:1] |
Generators of the group modulo torsion |
j |
-3153242386944/2000033 |
j-invariant |
L |
8.6915281884669 |
L(r)(E,1)/r! |
Ω |
1.3935323635194 |
Real period |
R |
0.51975399683372 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000068 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544l1 34272h1 68544r1 |
Quadratic twists by: -4 8 -3 |