Atkin-Lehner |
2- 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312ca |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1204224 |
Modular degree for the optimal curve |
Δ |
-773794486812672 = -1 · 218 · 37 · 13 · 473 |
Discriminant |
Eigenvalues |
2- 3+ 4 -5 -5 13+ -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,15839,-1101887] |
[a1,a2,a3,a4,a6] |
Generators |
[267:4700:1] |
Generators of the group modulo torsion |
j |
1676253304439/2951791713 |
j-invariant |
L |
4.1108655920917 |
L(r)(E,1)/r! |
Ω |
0.26473915829751 |
Real period |
R |
2.5879974145156 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000119006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bb1 29328bb1 |
Quadratic twists by: -4 8 |