Atkin-Lehner |
3+ 7- 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
72891b |
Isogeny class |
Conductor |
72891 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
68736 |
Modular degree for the optimal curve |
Δ |
-14506548147 = -1 · 39 · 72 · 132 · 89 |
Discriminant |
Eigenvalues |
0 3+ 4 7- 4 13+ -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1728,-28249] |
[a1,a2,a3,a4,a6] |
Generators |
[115:1137:1] |
Generators of the group modulo torsion |
j |
-28991029248/737009 |
j-invariant |
L |
7.9253753743827 |
L(r)(E,1)/r! |
Ω |
0.36968480182754 |
Real period |
R |
2.6797745450874 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001562 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72891a1 |
Quadratic twists by: -3 |