Atkin-Lehner |
5- 7- 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
51205m |
Isogeny class |
Conductor |
51205 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
282240 |
Modular degree for the optimal curve |
Δ |
-3189069898196875 = -1 · 55 · 79 · 113 · 19 |
Discriminant |
Eigenvalues |
0 -2 5- 7- 11+ -5 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,31785,-1609569] |
[a1,a2,a3,a4,a6] |
Generators |
[65:857:1] |
Generators of the group modulo torsion |
j |
88002363392/79028125 |
j-invariant |
L |
2.7911006248176 |
L(r)(E,1)/r! |
Ω |
0.24613514858077 |
Real period |
R |
1.1339707640174 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997886 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51205f1 |
Quadratic twists by: -7 |