Atkin-Lehner |
3- 5- 7- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
83475bo |
Isogeny class |
Conductor |
83475 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
522240 |
Modular degree for the optimal curve |
Δ |
684728048426625 = 316 · 53 · 74 · 53 |
Discriminant |
Eigenvalues |
-1 3- 5- 7- -4 4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-122945,-16513968] |
[a1,a2,a3,a4,a6] |
Generators |
[-210:206:1] [-196:255:1] |
Generators of the group modulo torsion |
j |
2255357919036221/7514162397 |
j-invariant |
L |
7.2137571745996 |
L(r)(E,1)/r! |
Ω |
0.25501111648508 |
Real period |
R |
3.5360013291379 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998755 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27825g1 83475bk1 |
Quadratic twists by: -3 5 |