Atkin-Lehner |
2+ 3- 19+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
36024d |
Isogeny class |
Conductor |
36024 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
36288 |
Modular degree for the optimal curve |
Δ |
-472706928 = -1 · 24 · 39 · 19 · 79 |
Discriminant |
Eigenvalues |
2+ 3- -4 0 0 -6 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3780,88209] |
[a1,a2,a3,a4,a6] |
Generators |
[36:9:1] [-36:423:1] |
Generators of the group modulo torsion |
j |
-373416940754176/29544183 |
j-invariant |
L |
8.242152501982 |
L(r)(E,1)/r! |
Ω |
1.5845867583853 |
Real period |
R |
0.28896957443208 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999977 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72048e1 108072j1 |
Quadratic twists by: -4 -3 |