Atkin-Lehner |
3- 5+ 31- 53- |
Signs for the Atkin-Lehner involutions |
Class |
123225p |
Isogeny class |
Conductor |
123225 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
857088 |
Modular degree for the optimal curve |
Δ |
-1314246610546875 = -1 · 36 · 58 · 31 · 533 |
Discriminant |
Eigenvalues |
-2 3- 5+ -1 -2 -6 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,17592,1501094] |
[a1,a2,a3,a4,a6] |
Generators |
[93:-1988:1] [-57:562:1] |
Generators of the group modulo torsion |
j |
38532274712576/84111783075 |
j-invariant |
L |
6.7463621016265 |
L(r)(E,1)/r! |
Ω |
0.3349977379083 |
Real period |
R |
0.55940362069583 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999870111 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24645b1 |
Quadratic twists by: 5 |