Atkin-Lehner |
2- 3+ 29- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
84912q |
Isogeny class |
Conductor |
84912 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
940032 |
Modular degree for the optimal curve |
Δ |
-1315489246038982656 = -1 · 229 · 33 · 293 · 612 |
Discriminant |
Eigenvalues |
2- 3+ 1 -1 0 0 -3 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1063080,-425127312] |
[a1,a2,a3,a4,a6] |
Generators |
[429254:4885978:343] |
Generators of the group modulo torsion |
j |
-32438593532957924521/321164366708736 |
j-invariant |
L |
5.7238271799049 |
L(r)(E,1)/r! |
Ω |
0.0742970638167 |
Real period |
R |
6.4199791189469 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000485 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10614g1 |
Quadratic twists by: -4 |