Atkin-Lehner |
5+ 7+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
112385b |
Isogeny class |
Conductor |
112385 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1919232 |
Modular degree for the optimal curve |
Δ |
-415321649121640625 = -1 · 57 · 73 · 138 · 19 |
Discriminant |
Eigenvalues |
1 -1 5+ 7+ 6 13+ -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-662483,209571562] |
[a1,a2,a3,a4,a6] |
Generators |
[1514:51010:1] |
Generators of the group modulo torsion |
j |
-6661757775617281/86044765625 |
j-invariant |
L |
4.377712632907 |
L(r)(E,1)/r! |
Ω |
0.29983568513766 |
Real period |
R |
7.3001862814189 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998224264 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8645a1 |
Quadratic twists by: 13 |