Atkin-Lehner |
2- 3- 5- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
12870cd |
Isogeny class |
Conductor |
12870 |
Conductor |
∏ cp |
512 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-3096135900000000 = -1 · 28 · 39 · 58 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- 5- -4 11+ 13- -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-22037,2963949] |
[a1,a2,a3,a4,a6] |
Generators |
[-163:1566:1] |
Generators of the group modulo torsion |
j |
-1623435815226889/4247100000000 |
j-invariant |
L |
6.6835279693128 |
L(r)(E,1)/r! |
Ω |
0.39693834838228 |
Real period |
R |
0.52617805735383 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
102960ev1 4290e1 64350ba1 |
Quadratic twists by: -4 -3 5 |