Atkin-Lehner |
2+ 3- 7- 31- |
Signs for the Atkin-Lehner involutions |
Class |
40362t |
Isogeny class |
Conductor |
40362 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-40880936171376 = -1 · 24 · 36 · 76 · 313 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -2 -2 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-13707,688870] |
[a1,a2,a3,a4,a6] |
Generators |
[80:-366:1] [-746:8979:8] |
Generators of the group modulo torsion |
j |
-9559173016567/1372257936 |
j-invariant |
L |
7.2965586352224 |
L(r)(E,1)/r! |
Ω |
0.62333891234153 |
Real period |
R |
0.32515567422283 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
121086bk1 40362h1 |
Quadratic twists by: -3 -31 |