Atkin-Lehner |
3- 5- 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
78585v |
Isogeny class |
Conductor |
78585 |
Conductor |
∏ cp |
180 |
Product of Tamagawa factors cp |
deg |
319680 |
Modular degree for the optimal curve |
Δ |
-129865789096875 = -1 · 39 · 55 · 133 · 312 |
Discriminant |
Eigenvalues |
-2 3- 5- -1 -1 13- -5 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-17320,1028824] |
[a1,a2,a3,a4,a6] |
Generators |
[-139:877:1] [-112:1255:1] |
Generators of the group modulo torsion |
j |
-261554618257408/59110509375 |
j-invariant |
L |
7.0193313193008 |
L(r)(E,1)/r! |
Ω |
0.55912022848681 |
Real period |
R |
0.069745795483667 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000104 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78585n1 |
Quadratic twists by: 13 |