Atkin-Lehner |
2+ 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
85176d |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-24288193972224 = -1 · 211 · 33 · 7 · 137 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7+ -3 13+ -1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-118131,-15629458] |
[a1,a2,a3,a4,a6] |
Generators |
[1714329214:315367016718:50653] |
Generators of the group modulo torsion |
j |
-683064198/91 |
j-invariant |
L |
7.4901054553945 |
L(r)(E,1)/r! |
Ω |
0.12875826551489 |
Real period |
R |
14.542960455674 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000664 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85176bi1 6552q1 |
Quadratic twists by: -3 13 |