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	4784d	Isogeny class
Conductor	4784	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-56336384 = -1 · 213 · 13 · 232	Discriminant
Eigenvalues	2-  1  3 -3 -2 13+ -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-224,1268]	[a1,a2,a3,a4,a6]
Generators	[-4:46:1]	Generators of the group modulo torsion
j	-304821217/13754	j-invariant
L	4.6561968212102	L(r)(E,1)/r!
Ω	1.965777394896	Real period
R	0.59215718337433	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	598c1 19136z1 43056ba1 119600bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4784d1

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
-	1	3	-3	-2	+	-1	4	-	0	-8	3	-2	1	3	-2	0	-4	10	-3	-12	-8	-6	-14	-12

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Quadratic twists for elliptic curve 4784d1

-4	8	-3	5	13	-23
598c1	19136z1	43056ba1	119600bf1	62192o1	110032j1

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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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