Cremona's table of elliptic curves

6006 = 2 · 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	6006c	Isogeny class
Conductor	6006	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	932323392 = 26 · 33 · 73 · 112 · 13	Discriminant
Eigenvalues	2+ 3+ -4 7+ 11+ 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2537,-50235]	[a1,a2,a3,a4,a6]
Generators	[-29:15:1]	Generators of the group modulo torsion
j	1806976738085401/932323392	j-invariant
L	1.5020595869377	L(r)(E,1)/r!
Ω	0.67268322804283	Real period
R	2.2329374723791	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	48048cz1 18018bg1 42042bi1 66066cc1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006c1

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	-4	-2	-2	0	4	-8	8	2	-4	8	10	-4	0	2	8	6	2	-10

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Quadratic twists for elliptic curve 6006c1

-4	-3	-7	-11	13
48048cz1	18018bg1	42042bi1	66066cc1	78078cr1

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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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