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	4872g	Isogeny class
Conductor	4872	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	220943407104 = 211 · 312 · 7 · 29	Discriminant
Eigenvalues	2+ 3- -2 7-  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8904,-325584]	[a1,a2,a3,a4,a6]
Generators	[267:4050:1]	Generators of the group modulo torsion
j	38123958498194/107882523	j-invariant
L	4.1943387992476	L(r)(E,1)/r!
Ω	0.49155608010839	Real period
R	2.8442592608645	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	9744a4 38976k4 14616p4 121800ba4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4872g3

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

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Quadratic twists for elliptic curve 4872g3

-4	8	-3	5	-7
9744a4	38976k4	14616p4	121800ba4	34104d4

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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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