Atkin-Lehner |
5+ 37- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
82325c |
Isogeny class |
Conductor |
82325 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
51520 |
Modular degree for the optimal curve |
Δ |
-1903765625 = -1 · 56 · 372 · 89 |
Discriminant |
Eigenvalues |
-1 -1 5+ 0 0 -4 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-6438,196156] |
[a1,a2,a3,a4,a6] |
Generators |
[49:12:1] [46:-20:1] |
Generators of the group modulo torsion |
j |
-1888690601881/121841 |
j-invariant |
L |
5.4428957255023 |
L(r)(E,1)/r! |
Ω |
1.4044230160113 |
Real period |
R |
1.9377693413803 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999836 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3293a1 |
Quadratic twists by: 5 |