Atkin-Lehner |
2- 3+ 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
129456w |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-1241501814226944 = -1 · 221 · 33 · 294 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 3 4 -5 -1 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,23469,-979182] |
[a1,a2,a3,a4,a6] |
Generators |
[22911:322944:343] |
Generators of the group modulo torsion |
j |
12926583470709/11225964032 |
j-invariant |
L |
9.6543730021618 |
L(r)(E,1)/r! |
Ω |
0.26709598797627 |
Real period |
R |
2.2591065885629 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000106384 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16182a1 129456bc1 |
Quadratic twists by: -4 -3 |