Atkin-Lehner |
2- 7- 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
65968q |
Isogeny class |
Conductor |
65968 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-162737692465954816 = -1 · 224 · 74 · 194 · 31 |
Discriminant |
Eigenvalues |
2- 0 -2 7- -4 -2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-98411,22757530] |
[a1,a2,a3,a4,a6] |
Generators |
[117:-3584:1] [183:3298:1] |
Generators of the group modulo torsion |
j |
-25733253533414337/39730881949696 |
j-invariant |
L |
8.7183505330415 |
L(r)(E,1)/r! |
Ω |
0.29003345811393 |
Real period |
R |
3.7574762019465 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999893 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8246d1 |
Quadratic twists by: -4 |