Atkin-Lehner |
2+ 3+ 7+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
3486a |
Isogeny class |
Conductor |
3486 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
20160 |
Modular degree for the optimal curve |
Δ |
-14695499258560512 = -1 · 215 · 38 · 77 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ 1 2 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,12495,5812821] |
[a1,a2,a3,a4,a6] |
Generators |
[159:3363:1] |
Generators of the group modulo torsion |
j |
215713926386390375/14695499258560512 |
j-invariant |
L |
2.1932285398723 |
L(r)(E,1)/r! |
Ω |
0.30115466907943 |
Real period |
R |
3.6413656586773 |
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 |
27888bk1 111552bi1 10458t1 87150cr1 |
Quadratic twists by: -4 8 -3 5 |