Atkin-Lehner |
2+ 3+ 5+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
33120a |
Isogeny class |
Conductor |
33120 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-60445656000 = -1 · 26 · 33 · 53 · 234 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 -2 -4 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-933,16132] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:160:1] [9:92:1] |
Generators of the group modulo torsion |
j |
-51978639168/34980125 |
j-invariant |
L |
7.6634368118679 |
L(r)(E,1)/r! |
Ω |
1.0237472296788 |
Real period |
R |
1.8714182050271 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33120v1 66240v1 33120z1 |
Quadratic twists by: -4 8 -3 |