Atkin-Lehner |
2+ 5- 7- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440bw |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-1951164006400 = -1 · 220 · 52 · 74 · 31 |
Discriminant |
Eigenvalues |
2+ 0 5- 7- -2 2 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-10412,-414416] |
[a1,a2,a3,a4,a6] |
j |
-476196576129/7443100 |
j-invariant |
L |
1.8887422288856 |
L(r)(E,1)/r! |
Ω |
0.23609277701101 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440dc1 2170m1 |
Quadratic twists by: -4 8 |