Atkin-Lehner |
3+ 13+ 17- 23- |
Signs for the Atkin-Lehner involutions |
Class |
15249b |
Isogeny class |
Conductor |
15249 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-40813538333053707 = -1 · 312 · 135 · 17 · 233 |
Discriminant |
Eigenvalues |
-2 3+ 2 -4 0 13+ 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-256582,51046194] |
[a1,a2,a3,a4,a6] |
Generators |
[541:8383:1] |
Generators of the group modulo torsion |
j |
-1868116528105864081408/40813538333053707 |
j-invariant |
L |
1.8418216214455 |
L(r)(E,1)/r! |
Ω |
0.36237420361499 |
Real period |
R |
0.84710850601015 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45747f1 |
Quadratic twists by: -3 |