Atkin-Lehner |
2- 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
74048u |
Isogeny class |
Conductor |
74048 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
189952 |
Modular degree for the optimal curve |
Δ |
91498381524992 = 214 · 137 · 89 |
Discriminant |
Eigenvalues |
2- -2 0 -1 2 13+ 7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-17733,-789725] |
[a1,a2,a3,a4,a6] |
Generators |
[-47322:221201:729] |
Generators of the group modulo torsion |
j |
37642192000000/5584618013 |
j-invariant |
L |
3.7626255367426 |
L(r)(E,1)/r! |
Ω |
0.41782339556166 |
Real period |
R |
9.0053012228056 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004716 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
74048d1 18512c1 |
Quadratic twists by: -4 8 |