Atkin-Lehner |
2+ 3- 5+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
12210o |
Isogeny class |
Conductor |
12210 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-8859504107520000 = -1 · 216 · 312 · 54 · 11 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 4 11+ -6 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-56909,6909896] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:3058:1] |
Generators of the group modulo torsion |
j |
-20382413355400899529/8859504107520000 |
j-invariant |
L |
4.2039242118874 |
L(r)(E,1)/r! |
Ω |
0.38541696355143 |
Real period |
R |
0.90895588618931 |
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 |
97680bi1 36630bt1 61050bn1 |
Quadratic twists by: -4 -3 5 |