Atkin-Lehner |
2+ 3+ 7+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
85008f |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
20480 |
Modular degree for the optimal curve |
Δ |
-4080384 = -1 · 28 · 32 · 7 · 11 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7+ 11- -2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-441,3717] |
[a1,a2,a3,a4,a6] |
Generators |
[12:3:1] |
Generators of the group modulo torsion |
j |
-37135043584/15939 |
j-invariant |
L |
4.5689411780995 |
L(r)(E,1)/r! |
Ω |
2.4305179897071 |
Real period |
R |
0.93991099839574 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999944204 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42504w1 |
Quadratic twists by: -4 |