Atkin-Lehner |
2+ 3+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712a |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-575668224 = -1 · 220 · 32 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -1 1 1 5 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-13121,-574143] |
[a1,a2,a3,a4,a6] |
Generators |
[239:3144:1] |
Generators of the group modulo torsion |
j |
-953054410321/2196 |
j-invariant |
L |
3.9943133251835 |
L(r)(E,1)/r! |
Ω |
0.22303602011078 |
Real period |
R |
4.4772065552456 |
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 |
11712bd1 366a1 35136i1 |
Quadratic twists by: -4 8 -3 |