Atkin-Lehner |
2+ 5+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
49600j |
Isogeny class |
Conductor |
49600 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-5079040000000000 = -1 · 224 · 510 · 31 |
Discriminant |
Eigenvalues |
2+ 2 5+ 0 -2 0 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-105633,-13616863] |
[a1,a2,a3,a4,a6] |
Generators |
[474163771191:1135957397500:1249243533] |
Generators of the group modulo torsion |
j |
-31824875809/1240000 |
j-invariant |
L |
8.6633058452539 |
L(r)(E,1)/r! |
Ω |
0.132107712714 |
Real period |
R |
16.394398304354 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000014 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49600ci1 1550c1 9920j1 |
Quadratic twists by: -4 8 5 |