Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
49686ck |
Isogeny class |
Conductor |
49686 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-3710585458944 = -1 · 28 · 36 · 76 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- -6 13+ 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3039,-114171] |
[a1,a2,a3,a4,a6] |
Generators |
[307:5138:1] |
Generators of the group modulo torsion |
j |
-156116857/186624 |
j-invariant |
L |
9.293571105215 |
L(r)(E,1)/r! |
Ω |
0.30743139918893 |
Real period |
R |
0.94467935872201 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1014f1 49686q1 |
Quadratic twists by: -7 13 |