Atkin-Lehner |
2+ 3+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
78078h |
Isogeny class |
Conductor |
78078 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
1769472 |
Modular degree for the optimal curve |
Δ |
-450905298658790976 = -1 · 26 · 34 · 74 · 118 · 132 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7+ 11- 13+ -5 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-386844,97921296] |
[a1,a2,a3,a4,a6] |
Generators |
[4112:258820:1] [-336:13956:1] |
Generators of the group modulo torsion |
j |
-37883173893317903137/2668078690288704 |
j-invariant |
L |
5.2551089036529 |
L(r)(E,1)/r! |
Ω |
0.29164207319338 |
Real period |
R |
0.2815474314871 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998061 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78078cj1 |
Quadratic twists by: 13 |