Atkin-Lehner |
2+ 3+ 7+ 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
32214b |
Isogeny class |
Conductor |
32214 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
75264 |
Modular degree for the optimal curve |
Δ |
-6512897664 = -1 · 27 · 36 · 7 · 132 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7+ 2 13+ -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-20456,1117632] |
[a1,a2,a3,a4,a6] |
Generators |
[83:-28:1] |
Generators of the group modulo torsion |
j |
-946714501733615497/6512897664 |
j-invariant |
L |
4.0274965065013 |
L(r)(E,1)/r! |
Ω |
1.1941190503104 |
Real period |
R |
0.84319409054196 |
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 |
96642bu1 |
Quadratic twists by: -3 |