Atkin-Lehner |
2- 29+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
68672z |
Isogeny class |
Conductor |
68672 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-236556910592 = -1 · 218 · 293 · 37 |
Discriminant |
Eigenvalues |
2- 3 2 -2 1 -4 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-844,25232] |
[a1,a2,a3,a4,a6] |
Generators |
[8832:159164:27] |
Generators of the group modulo torsion |
j |
-253636137/902393 |
j-invariant |
L |
12.723960665945 |
L(r)(E,1)/r! |
Ω |
0.86680303025644 |
Real period |
R |
7.339591707433 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000195 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68672i1 17168m1 |
Quadratic twists by: -4 8 |