Atkin-Lehner |
2+ 3- 7+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
51282i |
Isogeny class |
Conductor |
51282 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
3686400 |
Modular degree for the optimal curve |
Δ |
132814985579958528 = 28 · 315 · 74 · 11 · 372 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ 11+ 4 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-97473222,-370379997900] |
[a1,a2,a3,a4,a6] |
Generators |
[-673683267619360700:336980101730889222:118190052296875] |
Generators of the group modulo torsion |
j |
140492180287040918518806625/182187908888832 |
j-invariant |
L |
4.7099427606301 |
L(r)(E,1)/r! |
Ω |
0.048048321853362 |
Real period |
R |
24.506281275741 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999295 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17094x1 |
Quadratic twists by: -3 |