Atkin-Lehner |
2+ 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
104742a |
Isogeny class |
Conductor |
104742 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
85119451887888 = 24 · 33 · 113 · 236 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 11+ 2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-46122,-3775068] |
[a1,a2,a3,a4,a6] |
Generators |
[-129:189:1] [-116:122:1] |
Generators of the group modulo torsion |
j |
2714704875/21296 |
j-invariant |
L |
8.2192627461801 |
L(r)(E,1)/r! |
Ω |
0.32593238703072 |
Real period |
R |
12.608846301427 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000882 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
104742bg3 198d1 |
Quadratic twists by: -3 -23 |