Atkin-Lehner |
3- 7- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
48279u |
Isogeny class |
Conductor |
48279 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
35328 |
Modular degree for the optimal curve |
Δ |
-105586173 = -1 · 38 · 7 · 112 · 19 |
Discriminant |
Eigenvalues |
-1 3- 0 7- 11- -5 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-3198,69345] |
[a1,a2,a3,a4,a6] |
Generators |
[3:243:1] [33:-21:1] |
Generators of the group modulo torsion |
j |
-29893874547625/872613 |
j-invariant |
L |
7.4100379703729 |
L(r)(E,1)/r! |
Ω |
1.7530095818325 |
Real period |
R |
0.52837973956111 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48279n1 |
Quadratic twists by: -11 |