Atkin-Lehner |
2- 3+ 5+ 7- 43- |
Signs for the Atkin-Lehner involutions |
Class |
36120v |
Isogeny class |
Conductor |
36120 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
301056 |
Modular degree for the optimal curve |
Δ |
-26400501106963200 = -1 · 28 · 32 · 52 · 78 · 433 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -1 -7 1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,73719,1302525] |
[a1,a2,a3,a4,a6] |
Generators |
[-17:210:1] [1194:31605:8] |
Generators of the group modulo torsion |
j |
173067755625030656/103126957449075 |
j-invariant |
L |
7.2746737182859 |
L(r)(E,1)/r! |
Ω |
0.22964523757123 |
Real period |
R |
0.16498894563106 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72240o1 108360t1 |
Quadratic twists by: -4 -3 |