Atkin-Lehner |
2+ 3- 5+ 7- 73- |
Signs for the Atkin-Lehner involutions |
Class |
15330i |
Isogeny class |
Conductor |
15330 |
Conductor |
∏ cp |
108 |
Product of Tamagawa factors cp |
deg |
36288 |
Modular degree for the optimal curve |
Δ |
-49284263700 = -1 · 22 · 39 · 52 · 73 · 73 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- -6 -7 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1824,31666] |
[a1,a2,a3,a4,a6] |
Generators |
[-49:87:1] [-22:258:1] |
Generators of the group modulo torsion |
j |
-670588189536889/49284263700 |
j-invariant |
L |
5.6143029418609 |
L(r)(E,1)/r! |
Ω |
1.1081513598459 |
Real period |
R |
0.42219735989265 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
122640ba1 45990cj1 76650bt1 107310ba1 |
Quadratic twists by: -4 -3 5 -7 |