Atkin-Lehner |
2- 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384ce |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
117760 |
Modular degree for the optimal curve |
Δ |
-4233952100352 = -1 · 217 · 3 · 135 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 -5 13- 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5057,171873] |
[a1,a2,a3,a4,a6] |
Generators |
[91:676:1] |
Generators of the group modulo torsion |
j |
-109138636514/32302491 |
j-invariant |
L |
6.4818088603788 |
L(r)(E,1)/r! |
Ω |
0.73775288569004 |
Real period |
R |
0.87858807271723 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000893 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384bh1 18096l1 |
Quadratic twists by: -4 8 |