Atkin-Lehner |
3+ 5- 7+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
83475l |
Isogeny class |
Conductor |
83475 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1668096 |
Modular degree for the optimal curve |
Δ |
381728480089343625 = 39 · 53 · 7 · 536 |
Discriminant |
Eigenvalues |
-1 3+ 5- 7+ 0 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-6699485,-6672627908] |
[a1,a2,a3,a4,a6] |
Generators |
[-18225752:9015500:12167] |
Generators of the group modulo torsion |
j |
13515950827977125319/155150527903 |
j-invariant |
L |
3.0385470905493 |
L(r)(E,1)/r! |
Ω |
0.093840325189561 |
Real period |
R |
5.3966619868145 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999863895 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
83475k1 83475m1 |
Quadratic twists by: -3 5 |