Atkin-Lehner |
2+ 3+ 5+ 11- 101- |
Signs for the Atkin-Lehner involutions |
Class |
33330a |
Isogeny class |
Conductor |
33330 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-2922633207450 = -1 · 2 · 314 · 52 · 112 · 101 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -1 11- -4 -1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9213,-354033] |
[a1,a2,a3,a4,a6] |
Generators |
[321:5307:1] |
Generators of the group modulo torsion |
j |
-86496907136764249/2922633207450 |
j-invariant |
L |
2.4953585511512 |
L(r)(E,1)/r! |
Ω |
0.24316493145942 |
Real period |
R |
1.2827500126018 |
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 |
99990w1 |
Quadratic twists by: -3 |