Atkin-Lehner |
2- 3+ 7- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
122892o |
Isogeny class |
Conductor |
122892 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
456192 |
Modular degree for the optimal curve |
Δ |
143953313543424 = 28 · 33 · 77 · 113 · 19 |
Discriminant |
Eigenvalues |
2- 3+ -3 7- 11- 4 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-15157,-422351] |
[a1,a2,a3,a4,a6] |
Generators |
[-37:-294:1] [-72:539:1] |
Generators of the group modulo torsion |
j |
12786860032/4779621 |
j-invariant |
L |
8.759814166634 |
L(r)(E,1)/r! |
Ω |
0.44389679111126 |
Real period |
R |
0.54816384383356 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000594 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17556o1 |
Quadratic twists by: -7 |