Atkin-Lehner |
2- 3+ 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
72072y |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
100 |
Product of Tamagawa factors cp |
deg |
556800 |
Modular degree for the optimal curve |
Δ |
-345884343890012928 = -1 · 28 · 39 · 75 · 11 · 135 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- 11- 13- 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-274860,62265348] |
[a1,a2,a3,a4,a6] |
Generators |
[432:4914:1] |
Generators of the group modulo torsion |
j |
-455750423424000/68643535961 |
j-invariant |
L |
6.9073280638554 |
L(r)(E,1)/r! |
Ω |
0.29302297189075 |
Real period |
R |
0.23572650361786 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999281 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72072e1 |
Quadratic twists by: -3 |