Atkin-Lehner |
2- 3- 19+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
48336bj |
Isogeny class |
Conductor |
48336 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
77760 |
Modular degree for the optimal curve |
Δ |
114484831056 = 24 · 39 · 193 · 53 |
Discriminant |
Eigenvalues |
2- 3- -1 -3 -2 -2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-44441,-3620802] |
[a1,a2,a3,a4,a6] |
Generators |
[-122:6:1] |
Generators of the group modulo torsion |
j |
606687392623673344/7155301941 |
j-invariant |
L |
5.1671360058897 |
L(r)(E,1)/r! |
Ω |
0.32881611360538 |
Real period |
R |
1.7460404132359 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999734 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12084a1 |
Quadratic twists by: -4 |