Cremona's table of elliptic curves

4872 = 2³ · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	4872c	Isogeny class
Conductor	4872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-1091328 = -1 · 28 · 3 · 72 · 29	Discriminant
Eigenvalues	2+ 3+ -4 7+ -4  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,20,-44]	[a1,a2,a3,a4,a6]
Generators	[6:16:1]	Generators of the group modulo torsion
j	3286064/4263	j-invariant
L	2.1509942197269	L(r)(E,1)/r!
Ω	1.4722155624197	Real period
R	1.4610592868557	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	9744f1 38976t1 14616n1 121800bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4872c1

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	+	-4	2	-2	8	-2	+	0	2	-10	2	8	6	0	12	4	2	0	-6	16	2	0

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Quadratic twists for elliptic curve 4872c1

-4	8	-3	5	-7
9744f1	38976t1	14616n1	121800bq1	34104r1

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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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