Atkin-Lehner |
2+ 3- 7+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
47712i |
Isogeny class |
Conductor |
47712 |
Conductor |
∏ cp |
5 |
Product of Tamagawa factors cp |
deg |
14080 |
Modular degree for the optimal curve |
Δ |
-61834752 = -1 · 29 · 35 · 7 · 71 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ -4 4 0 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-232,-1492] |
[a1,a2,a3,a4,a6] |
Generators |
[47:306:1] |
Generators of the group modulo torsion |
j |
-2708870984/120771 |
j-invariant |
L |
8.2648760916321 |
L(r)(E,1)/r! |
Ω |
0.6098336674358 |
Real period |
R |
2.7105345384919 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000039 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47712b1 95424br1 |
Quadratic twists by: -4 8 |