Atkin-Lehner |
7+ 19- 29- |
Signs for the Atkin-Lehner involutions |
Class |
3857a |
Isogeny class |
Conductor |
3857 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1728 |
Modular degree for the optimal curve |
Δ |
-185186141 = -1 · 72 · 194 · 29 |
Discriminant |
Eigenvalues |
1 -3 1 7+ -3 -1 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-364,-2663] |
[a1,a2,a3,a4,a6] |
Generators |
[32:117:1] |
Generators of the group modulo torsion |
j |
-5341937695641/185186141 |
j-invariant |
L |
2.5132440205576 |
L(r)(E,1)/r! |
Ω |
0.54532344023088 |
Real period |
R |
0.57609022351339 |
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 |
61712k1 34713f1 96425j1 26999h1 |
Quadratic twists by: -4 -3 5 -7 |