Atkin-Lehner |
2+ 3+ 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
78078r |
Isogeny class |
Conductor |
78078 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
389376 |
Modular degree for the optimal curve |
Δ |
1163390259905874 = 2 · 33 · 74 · 11 · 138 |
Discriminant |
Eigenvalues |
2+ 3+ 1 7- 11- 13+ -1 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-61012,-5589098] |
[a1,a2,a3,a4,a6] |
Generators |
[-163:323:1] |
Generators of the group modulo torsion |
j |
30791709481/1426194 |
j-invariant |
L |
4.2869304251919 |
L(r)(E,1)/r! |
Ω |
0.30464129266749 |
Real period |
R |
3.5180148968388 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000468 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78078bt1 |
Quadratic twists by: 13 |