Atkin-Lehner |
5+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
7865c |
Isogeny class |
Conductor |
7865 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
983125 = 54 · 112 · 13 |
Discriminant |
Eigenvalues |
-1 3 5+ -2 11- 13- -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-243,-1394] |
[a1,a2,a3,a4,a6] |
Generators |
[-240:119:27] |
Generators of the group modulo torsion |
j |
13064132169/8125 |
j-invariant |
L |
4.1112999653896 |
L(r)(E,1)/r! |
Ω |
1.2096338046036 |
Real period |
R |
1.6993985906077 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
125840cb1 70785be1 39325c1 7865a1 |
Quadratic twists by: -4 -3 5 -11 |