Atkin-Lehner |
2+ 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
129712k |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
36480 |
Modular degree for the optimal curve |
Δ |
-15695152 = -1 · 24 · 114 · 67 |
Discriminant |
Eigenvalues |
2+ 2 0 4 11- 0 2 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-403,3258] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:66:1] |
Generators of the group modulo torsion |
j |
-30976000/67 |
j-invariant |
L |
12.259221141999 |
L(r)(E,1)/r! |
Ω |
2.2116310844973 |
Real period |
R |
1.8476892780833 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000013292 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64856i1 129712l1 |
Quadratic twists by: -4 -11 |