Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
51984ce |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
766080 |
Modular degree for the optimal curve |
Δ |
-7708322420519436288 = -1 · 215 · 36 · 199 |
Discriminant |
Eigenvalues |
2- 3- -2 3 -2 -3 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-61731,133709346] |
[a1,a2,a3,a4,a6] |
Generators |
[-1135345:57217778:4913] |
Generators of the group modulo torsion |
j |
-27/8 |
j-invariant |
L |
5.5610886824988 |
L(r)(E,1)/r! |
Ω |
0.19055302746512 |
Real period |
R |
7.2959857375036 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6498f1 5776k1 51984cd1 |
Quadratic twists by: -4 -3 -19 |