Atkin-Lehner |
2- 3- 5- 11+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
72270bi |
Isogeny class |
Conductor |
72270 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
188416 |
Modular degree for the optimal curve |
Δ |
10976006250000 = 24 · 37 · 58 · 11 · 73 |
Discriminant |
Eigenvalues |
2- 3- 5- 0 11+ 6 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-7952,-219549] |
[a1,a2,a3,a4,a6] |
Generators |
[-61:219:1] |
Generators of the group modulo torsion |
j |
76273573823929/15056250000 |
j-invariant |
L |
11.184280440972 |
L(r)(E,1)/r! |
Ω |
0.51253998776098 |
Real period |
R |
2.7276604530063 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994389 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
24090c1 |
Quadratic twists by: -3 |