Atkin-Lehner |
2- 3- 7+ 11- 61- |
Signs for the Atkin-Lehner involutions |
Class |
84546bp |
Isogeny class |
Conductor |
84546 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
774144 |
Modular degree for the optimal curve |
Δ |
-5420670886084608 = -1 · 218 · 38 · 7 · 112 · 612 |
Discriminant |
Eigenvalues |
2- 3- -4 7+ 11- -2 -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,27058,-3107235] |
[a1,a2,a3,a4,a6] |
Generators |
[177:-2773:1] |
Generators of the group modulo torsion |
j |
3005372501552231/7435762532352 |
j-invariant |
L |
5.693624172796 |
L(r)(E,1)/r! |
Ω |
0.22150761500681 |
Real period |
R |
0.71399905104157 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006877 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28182c1 |
Quadratic twists by: -3 |