Cremona's table of elliptic curves

4784 = 2⁴ · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 13- 23+	Signs for the Atkin-Lehner involutions
Class	4784f	Isogeny class
Conductor	4784	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-476831154176 = -1 · 217 · 13 · 234	Discriminant
Eigenvalues	2-  3 -3 -3  2 13-  1 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,701,-32446]	[a1,a2,a3,a4,a6]
Generators	[1947:16928:27]	Generators of the group modulo torsion
j	9300746727/116413856	j-invariant
L	4.9739527581105	L(r)(E,1)/r!
Ω	0.45851767001611	Real period
R	1.355987207084	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	598b1 19136t1 43056by1 119600y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4784f1

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
-	3	-3	-3	2	-	1	-6	+	-6	4	-7	4	9	5	-12	-14	0	2	3	-10	-16	-16	2	-14

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Quadratic twists for elliptic curve 4784f1

-4	8	-3	5	13	-23
598b1	19136t1	43056by1	119600y1	62192m1	110032r1

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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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