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	6336b	Isogeny class
Conductor	6336	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	150730702848 = 222 · 33 · 113	Discriminant
Eigenvalues	2+ 3+  0  2 11+ -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5580,159344]	[a1,a2,a3,a4,a6]
Generators	[-82:256:1]	Generators of the group modulo torsion
j	2714704875/21296	j-invariant
L	4.273397307491	L(r)(E,1)/r!
Ω	1.0334688009988	Real period
R	2.0675018459005	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	6336bp1 198d1 6336g3 69696l1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336b1

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
+	+	0	2	+	-2	6	-2	0	-6	-4	-2	-6	10	-12	-12	12	10	-8	-12	14	2	-12	0	2

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Quadratic twists for elliptic curve 6336b1

-4	8	-3	-11
6336bp1	198d1	6336g3	69696l1

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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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