Cremona's table of elliptic curves

4503 = 3 · 19 · 79

Field	Data	Notes
Atkin-Lehner	3+ 19+ 79+	Signs for the Atkin-Lehner involutions
Class	4503a	Isogeny class
Conductor	4503	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	14976	Modular degree for the optimal curve
Δ	-45939934165131 = -1 · 318 · 19 · 792	Discriminant
Eigenvalues	0 3+ -3 -3  5 -4 -7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,4223,-309933]	[a1,a2,a3,a4,a6]
Generators	[457:9841:1]	Generators of the group modulo torsion
j	8326914628124672/45939934165131	j-invariant
L	1.6276828962285	L(r)(E,1)/r!
Ω	0.3201931385317	Real period
R	1.2708602249353	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	72048ba1 13509a1 112575g1 85557e1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4503a1

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
0	+	-3	-3	5	-4	-7	+	0	2	6	6	10	1	-7	12	4	5	2	6	-7	+	-12	16	-18

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Quadratic twists for elliptic curve 4503a1

-4	-3	5	-19
72048ba1	13509a1	112575g1	85557e1

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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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