Atkin-Lehner |
3+ 5- 7- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
83475m |
Isogeny class |
Conductor |
83475 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8340480 |
Modular degree for the optimal curve |
Δ |
5.964507501396E+21 |
Discriminant |
Eigenvalues |
1 3+ 5- 7- 0 2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-167487117,-834245975584] |
[a1,a2,a3,a4,a6] |
Generators |
[-36196565961976811108359365295199036777312953974833426857786739744:23334052756165452434209621363688179556153245870459596608325505872:4833023621588885884184807743774378129186045760309629134092549] |
Generators of the group modulo torsion |
j |
13515950827977125319/155150527903 |
j-invariant |
L |
8.1896346257134 |
L(r)(E,1)/r! |
Ω |
0.041966669230909 |
Real period |
R |
97.573083303948 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
83475p1 83475l1 |
Quadratic twists by: -3 5 |