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	4503d	Isogeny class
Conductor	4503	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-13509 = -1 · 32 · 19 · 79	Discriminant
Eigenvalues	-1 3-  3  0  0 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-19,-34]	[a1,a2,a3,a4,a6]
Generators	[5:-1:1]	Generators of the group modulo torsion
j	-761048497/13509	j-invariant
L	3.3801429044468	L(r)(E,1)/r!
Ω	1.1418386730044	Real period
R	1.4801315563927	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	72048n1 13509d1 112575a1 85557b1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4503d1

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	0	0	-2	-2	+	-2	-7	-5	-5	-3	-1	7	-11	-14	0	3	-12	11	-	0	-4	8

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Quadratic twists for elliptic curve 4503d1

-4	-3	5	-19
72048n1	13509d1	112575a1	85557b1

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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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