Atkin-Lehner |
2+ 3+ 5- 7+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
61320i |
Isogeny class |
Conductor |
61320 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
135936 |
Modular degree for the optimal curve |
Δ |
-1201872000000 = -1 · 210 · 3 · 56 · 73 · 73 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7+ 2 1 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-19080,1022172] |
[a1,a2,a3,a4,a6] |
Generators |
[74:-100:1] |
Generators of the group modulo torsion |
j |
-750207891394084/1173703125 |
j-invariant |
L |
5.5372558216043 |
L(r)(E,1)/r! |
Ω |
0.86424085534739 |
Real period |
R |
0.53392290152669 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000622 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122640x1 |
Quadratic twists by: -4 |