Atkin-Lehner |
2+ 3+ 5- 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
51240c |
Isogeny class |
Conductor |
51240 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
204960000 = 28 · 3 · 54 · 7 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- -4 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-460,3892] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:80:1] |
Generators of the group modulo torsion |
j |
42140629456/800625 |
j-invariant |
L |
4.669075755075 |
L(r)(E,1)/r! |
Ω |
1.7830165954481 |
Real period |
R |
1.3093192085325 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999362 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
102480s1 |
Quadratic twists by: -4 |