Cremona's table of elliptic curves

6336 = 2⁶ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	6336bu	Isogeny class
Conductor	6336	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	56757583872 = 218 · 39 · 11	Discriminant
Eigenvalues	2- 3+ -4  2 11-  2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-972,-2160]	[a1,a2,a3,a4,a6]
Generators	[-3:27:1]	Generators of the group modulo torsion
j	19683/11	j-invariant
L	3.295052434207	L(r)(E,1)/r!
Ω	0.91824285034095	Real period
R	1.7942162212227	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6336e1 1584i1 6336bn1 69696ew1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336bu1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-4	2	-	2	-2	-6	4	-6	-4	6	10	6	-8	0	-4	6	8	0	-2	10	-12	0	2

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Quadratic twists for elliptic curve 6336bu1

-4	8	-3	-11
6336e1	1584i1	6336bn1	69696ew1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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