Atkin-Lehner |
2+ 3- 5- 23- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
126270u |
Isogeny class |
Conductor |
126270 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
114688 |
Modular degree for the optimal curve |
Δ |
30683610000 = 24 · 37 · 54 · 23 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 -4 -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1089,11245] |
[a1,a2,a3,a4,a6] |
Generators |
[-282:701:8] [-34:107:1] |
Generators of the group modulo torsion |
j |
196021690129/42090000 |
j-invariant |
L |
9.5585391606772 |
L(r)(E,1)/r! |
Ω |
1.1089553569575 |
Real period |
R |
1.0774260543954 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002823 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42090m1 |
Quadratic twists by: -3 |