Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
113568by |
Isogeny class |
Conductor |
113568 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-7212022272 = -1 · 29 · 35 · 73 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 0 13+ 7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,48,4068] |
[a1,a2,a3,a4,a6] |
Generators |
[8:70:1] |
Generators of the group modulo torsion |
j |
138424/83349 |
j-invariant |
L |
8.0458087983674 |
L(r)(E,1)/r! |
Ω |
1.0319650335014 |
Real period |
R |
1.299431751415 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000016252 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
113568z1 113568d1 |
Quadratic twists by: -4 13 |