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	24	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-481275648 = -1 · 28 · 33 · 74 · 29	Discriminant
Eigenvalues	2+ 3- -2 7-  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,196,0]	[a1,a2,a3,a4,a6]
Generators	[7:42:1]	Generators of the group modulo torsion
j	3236192048/1879983	j-invariant
L	4.1943387992476	L(r)(E,1)/r!
Ω	0.98311216021677	Real period
R	0.71106481521613	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	9744a1 38976k1 14616p1 121800ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4872g1

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 4872g1

-4	8	-3	5	-7
9744a1	38976k1	14616p1	121800ba1	34104d1

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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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