Atkin-Lehner |
2- 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312cc |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
3317760 |
Modular degree for the optimal curve |
Δ |
-90042145333051392 = -1 · 218 · 39 · 135 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 1 5 13- 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-12057793,-16111712927] |
[a1,a2,a3,a4,a6] |
Generators |
[20793949347:76938647680:5177717] |
Generators of the group modulo torsion |
j |
-739583643739785288625/343483525593 |
j-invariant |
L |
7.4197946412724 |
L(r)(E,1)/r! |
Ω |
0.040509099390012 |
Real period |
R |
18.316365342602 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bi1 29328n1 |
Quadratic twists by: -4 8 |