Cremona's table of elliptic curves

4738 = 2 · 23 · 103

Field	Data	Notes
Atkin-Lehner	2+ 23+ 103+	Signs for the Atkin-Lehner involutions
Class	4738a	Isogeny class
Conductor	4738	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-37904 = -1 · 24 · 23 · 103	Discriminant
Eigenvalues	2+ -1  3  1  4 -2 -8  3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-11,13]	[a1,a2,a3,a4,a6]
Generators	[2:1:1]	Generators of the group modulo torsion
j	-169112377/37904	j-invariant
L	2.8945012522693	L(r)(E,1)/r!
Ω	3.484789805371	Real period
R	0.41530499885648	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	37904h1 42642p1 118450n1 108974c1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4738a1

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	1	4	-2	-8	3	+	-7	1	5	1	0	-4	-14	-10	6	-8	-5	0	-4	5	-6	-8

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Quadratic twists for elliptic curve 4738a1

-4	-3	5	-23
37904h1	42642p1	118450n1	108974c1

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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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