Atkin-Lehner |
2+ 3+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312a |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
-1228137308356608 = -1 · 234 · 32 · 132 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 0 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5793,1696545] |
[a1,a2,a3,a4,a6] |
Generators |
[159:2184:1] |
Generators of the group modulo torsion |
j |
-82029363625/4684972032 |
j-invariant |
L |
4.8079229680404 |
L(r)(E,1)/r! |
Ω |
0.40167914406862 |
Real period |
R |
2.9923902164013 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000009706 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117312cs1 3666i1 |
Quadratic twists by: -4 8 |