Atkin-Lehner |
3- 5+ 7+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
15225p |
Isogeny class |
Conductor |
15225 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-81596484375 = -1 · 3 · 58 · 74 · 29 |
Discriminant |
Eigenvalues |
1 3- 5+ 7+ -4 2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,724,11573] |
[a1,a2,a3,a4,a6] |
Generators |
[31829:305682:343] |
Generators of the group modulo torsion |
j |
2691419471/5222175 |
j-invariant |
L |
6.4217991629813 |
L(r)(E,1)/r! |
Ω |
0.74626219587994 |
Real period |
R |
8.6052853788328 |
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 |
45675j1 3045d1 106575t1 |
Quadratic twists by: -3 5 -7 |