Atkin-Lehner |
3+ 7- 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
72891a |
Isogeny class |
Conductor |
72891 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
22912 |
Modular degree for the optimal curve |
Δ |
-19899243 = -1 · 33 · 72 · 132 · 89 |
Discriminant |
Eigenvalues |
0 3+ -4 7- -4 13+ 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-192,1046] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:353:8] [-8:45:1] |
Generators of the group modulo torsion |
j |
-28991029248/737009 |
j-invariant |
L |
6.5700628500078 |
L(r)(E,1)/r! |
Ω |
2.1601665910237 |
Real period |
R |
0.38018264871708 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000066 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72891b1 |
Quadratic twists by: -3 |