Cremona's table of elliptic curves

6216 = 2³ · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 37-	Signs for the Atkin-Lehner involutions
Class	6216m	Isogeny class
Conductor	6216	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3584	Modular degree for the optimal curve
Δ	-4408026672 = -1 · 24 · 3 · 72 · 374	Discriminant
Eigenvalues	2- 3+  2 7+ -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-407,4632]	[a1,a2,a3,a4,a6]
Generators	[1:65:1]	Generators of the group modulo torsion
j	-467147020288/275501667	j-invariant
L	3.6462886159783	L(r)(E,1)/r!
Ω	1.2789554590932	Real period
R	2.8509895243449	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12432t1 49728bl1 18648i1 43512bn1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6216m1

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

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Quadratic twists for elliptic curve 6216m1

-4	8	-3	-7
12432t1	49728bl1	18648i1	43512bn1

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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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