Cremona's table of elliptic curves

4505 = 5 · 17 · 53

Field	Data	Notes
Atkin-Lehner	5+ 17- 53+	Signs for the Atkin-Lehner involutions
Class	4505a	Isogeny class
Conductor	4505	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	5088	Modular degree for the optimal curve
Δ	1301945 = 5 · 173 · 53	Discriminant
Eigenvalues	1 -2 5+  0 -2 -6 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-27124,1717101]	[a1,a2,a3,a4,a6]
Generators	[99:18:1] [-1418:8559:8]	Generators of the group modulo torsion
j	2206794549237788089/1301945	j-invariant
L	4.0361041044245	L(r)(E,1)/r!
Ω	1.6672311476013	Real period
R	3.2277900679669	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	72080e1 40545i1 22525f1 76585b1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4505a1

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	-2	+	0	-2	-6	-	-6	-2	-6	-8	-6	-2	-10	2	+	0	-2	-4	4	-6	8	0	-6	14

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Quadratic twists for elliptic curve 4505a1

-4	-3	5	17
72080e1	40545i1	22525f1	76585b1

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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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