Atkin-Lehner |
2+ 3+ 29+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
49416a |
Isogeny class |
Conductor |
49416 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
177216 |
Modular degree for the optimal curve |
Δ |
-3136223358792432 = -1 · 24 · 313 · 293 · 712 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -3 3 3 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-47888,-4834779] |
[a1,a2,a3,a4,a6] |
Generators |
[69870:1493343:125] |
Generators of the group modulo torsion |
j |
-759089347482784000/196013959924527 |
j-invariant |
L |
4.6346029314775 |
L(r)(E,1)/r! |
Ω |
0.15921094985123 |
Real period |
R |
7.2774563179072 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999527 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
98832c1 |
Quadratic twists by: -4 |