Atkin-Lehner |
2+ 3+ 43+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
48504a |
Isogeny class |
Conductor |
48504 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
2429500779058176 = 210 · 312 · 43 · 473 |
Discriminant |
Eigenvalues |
2+ 3+ -1 2 0 0 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-34016,-444036] |
[a1,a2,a3,a4,a6] |
Generators |
[1610:64152:1] |
Generators of the group modulo torsion |
j |
4250952491294596/2372559354549 |
j-invariant |
L |
4.6821482664759 |
L(r)(E,1)/r! |
Ω |
0.37738646077931 |
Real period |
R |
3.101693325733 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999812 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
97008m1 |
Quadratic twists by: -4 |