Atkin-Lehner |
7+ 11- 41- |
Signs for the Atkin-Lehner involutions |
Class |
3157a |
Isogeny class |
Conductor |
3157 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
144 |
Modular degree for the optimal curve |
Δ |
-3157 = -1 · 7 · 11 · 41 |
Discriminant |
Eigenvalues |
1 -2 0 7+ 11- 2 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1,-3] |
[a1,a2,a3,a4,a6] |
Generators |
[3:3:1] |
Generators of the group modulo torsion |
j |
-15625/3157 |
j-invariant |
L |
2.7962622802528 |
L(r)(E,1)/r! |
Ω |
2.0010523071801 |
Real period |
R |
1.3973958952594 |
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 |
50512k1 28413c1 78925h1 22099c1 |
Quadratic twists by: -4 -3 5 -7 |