Atkin-Lehner |
2- 3+ 5+ 11- 73- |
Signs for the Atkin-Lehner involutions |
Class |
72270v |
Isogeny class |
Conductor |
72270 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
107454504960000 = 216 · 33 · 54 · 113 · 73 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 11- -2 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-12473,199897] |
[a1,a2,a3,a4,a6] |
Generators |
[151:-1396:1] [-97:748:1] |
Generators of the group modulo torsion |
j |
7947674497946547/3979796480000 |
j-invariant |
L |
13.355082244799 |
L(r)(E,1)/r! |
Ω |
0.52650540910409 |
Real period |
R |
0.5284482842709 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999849 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72270f1 |
Quadratic twists by: -3 |