Atkin-Lehner |
2+ 3- 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
72072n |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
270336 |
Modular degree for the optimal curve |
Δ |
-46711436099328 = -1 · 28 · 312 · 74 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -4 7+ 11- 13- -4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-15447,808810] |
[a1,a2,a3,a4,a6] |
Generators |
[2:882:1] [47:432:1] |
Generators of the group modulo torsion |
j |
-2184181167184/250297047 |
j-invariant |
L |
8.0819190816805 |
L(r)(E,1)/r! |
Ω |
0.61989341689578 |
Real period |
R |
3.2593986568344 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000047 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24024z1 |
Quadratic twists by: -3 |