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	6336br	Isogeny class
Conductor	6336	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-78041677824 = -1 · 215 · 39 · 112	Discriminant
Eigenvalues	2- 3+  2 -4 11- -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,756,-10800]	[a1,a2,a3,a4,a6]
Generators	[13:35:1]	Generators of the group modulo torsion
j	74088/121	j-invariant
L	4.0763762542333	L(r)(E,1)/r!
Ω	0.5722391912461	Real period
R	3.5617765408174	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	6336bk2 3168d2 6336bm2 69696en2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336br2

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
-	+	2	-4	-	-4	6	-2	6	2	-8	-6	2	6	-2	6	-8	12	-4	-14	-10	-8	-4	8	-10

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Quadratic twists for elliptic curve 6336br2

-4	8	-3	-11
6336bk2	3168d2	6336bm2	69696en2

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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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