Atkin-Lehner |
2- 3- 5- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
81840dj |
Isogeny class |
Conductor |
81840 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
77319320688720 = 24 · 32 · 5 · 112 · 316 |
Discriminant |
Eigenvalues |
2- 3- 5- -2 11+ 4 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-11745,243198] |
[a1,a2,a3,a4,a6] |
Generators |
[378:7068:1] |
Generators of the group modulo torsion |
j |
11199529273409536/4832457543045 |
j-invariant |
L |
8.6492661734 |
L(r)(E,1)/r! |
Ω |
0.55117193648624 |
Real period |
R |
2.6154168354605 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002177 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20460e1 |
Quadratic twists by: -4 |