Atkin-Lehner |
7+ 37+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
12173b |
Isogeny class |
Conductor |
12173 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3584 |
Modular degree for the optimal curve |
Δ |
-85211 = -1 · 72 · 37 · 47 |
Discriminant |
Eigenvalues |
-2 -3 -3 7+ 0 1 -4 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,11,0] |
[a1,a2,a3,a4,a6] |
Generators |
[0:0:1] [1:3:1] |
Generators of the group modulo torsion |
j |
147197952/85211 |
j-invariant |
L |
1.7849648534763 |
L(r)(E,1)/r! |
Ω |
2.0408830131693 |
Real period |
R |
0.43730209961953 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000016 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
109557g1 85211g1 |
Quadratic twists by: -3 -7 |