Atkin-Lehner |
2- 3- 5- 17- |
Signs for the Atkin-Lehner involutions |
Class |
69360dz |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
1762560 |
Modular degree for the optimal curve |
Δ |
-694316670223564800 = -1 · 214 · 35 · 52 · 178 |
Discriminant |
Eigenvalues |
2- 3- 5- -3 -6 -7 17- 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-617400,-191184300] |
[a1,a2,a3,a4,a6] |
Generators |
[1830:-69360:1] |
Generators of the group modulo torsion |
j |
-910904761/24300 |
j-invariant |
L |
5.5145173365718 |
L(r)(E,1)/r! |
Ω |
0.085024514084582 |
Real period |
R |
0.54048307872084 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997651 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8670f1 69360cg1 |
Quadratic twists by: -4 17 |