Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744v |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-283527415759053312 = -1 · 29 · 38 · 78 · 114 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 11- -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-134472,-31838652] |
[a1,a2,a3,a4,a6] |
Generators |
[7328:626450:1] |
Generators of the group modulo torsion |
j |
-4464412682696/4706920449 |
j-invariant |
L |
6.16327671797 |
L(r)(E,1)/r! |
Ω |
0.11964232269712 |
Real period |
R |
6.439273096499 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744ci2 103488dh3 7392e4 |
Quadratic twists by: -4 8 -7 |