Atkin-Lehner |
3- 13+ 19+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
51129d |
Isogeny class |
Conductor |
51129 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
79872 |
Modular degree for the optimal curve |
Δ |
-745721731287 = -1 · 312 · 132 · 192 · 23 |
Discriminant |
Eigenvalues |
1 3- 2 0 -6 13+ -8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,504,-41445] |
[a1,a2,a3,a4,a6] |
Generators |
[78:645:1] [2190:35175:8] |
Generators of the group modulo torsion |
j |
19400056703/1022937903 |
j-invariant |
L |
12.198492713912 |
L(r)(E,1)/r! |
Ω |
0.43051277955998 |
Real period |
R |
7.0836995398714 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17043d1 |
Quadratic twists by: -3 |