Atkin-Lehner |
3+ 5- 11+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
10065d |
Isogeny class |
Conductor |
10065 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-24517297014375 = -1 · 3 · 54 · 118 · 61 |
Discriminant |
Eigenvalues |
1 3+ 5- -4 11+ -2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2497,241984] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:526:1] |
Generators of the group modulo torsion |
j |
-1722864296274841/24517297014375 |
j-invariant |
L |
3.8841303574019 |
L(r)(E,1)/r! |
Ω |
0.56945187753355 |
Real period |
R |
3.4104114066891 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
30195i1 50325t1 110715g1 |
Quadratic twists by: -3 5 -11 |