Atkin-Lehner |
3+ 5+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
39975a |
Isogeny class |
Conductor |
39975 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
451008 |
Modular degree for the optimal curve |
Δ |
872441884691325 = 318 · 52 · 133 · 41 |
Discriminant |
Eigenvalues |
0 3+ 5+ -5 3 13+ -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-269103,53802128] |
[a1,a2,a3,a4,a6] |
Generators |
[-402:9841:1] |
Generators of the group modulo torsion |
j |
86206683096332861440/34897675387653 |
j-invariant |
L |
1.6498445442728 |
L(r)(E,1)/r! |
Ω |
0.49107136591464 |
Real period |
R |
1.6798419321399 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999974 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
119925s1 39975y1 |
Quadratic twists by: -3 5 |