Atkin-Lehner |
2- 3+ 29- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
84912s |
Isogeny class |
Conductor |
84912 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
569856 |
Modular degree for the optimal curve |
Δ |
-1933287284736 = -1 · 213 · 37 · 29 · 612 |
Discriminant |
Eigenvalues |
2- 3+ -3 -5 6 2 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-78752,8532864] |
[a1,a2,a3,a4,a6] |
Generators |
[184:488:1] |
Generators of the group modulo torsion |
j |
-13187244395666593/471993966 |
j-invariant |
L |
4.0523796691109 |
L(r)(E,1)/r! |
Ω |
0.777687257802 |
Real period |
R |
0.65135111067342 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999903851 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10614r1 |
Quadratic twists by: -4 |