Atkin-Lehner |
2+ 3+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
83664j |
Isogeny class |
Conductor |
83664 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
39936 |
Modular degree for the optimal curve |
Δ |
1020784464 = 24 · 33 · 73 · 832 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- -6 -4 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-426,3015] |
[a1,a2,a3,a4,a6] |
Generators |
[3:42:1] [31:140:1] |
Generators of the group modulo torsion |
j |
19791046656/2362927 |
j-invariant |
L |
9.5490355247564 |
L(r)(E,1)/r! |
Ω |
1.5063205243073 |
Real period |
R |
2.11310394446 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000016 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
41832b1 83664l1 |
Quadratic twists by: -4 -3 |