Cremona's table of elliptic curves

17760 = 2⁵ · 3 · 5 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	17760l	Isogeny class
Conductor	17760	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	44928	Modular degree for the optimal curve
Δ	-20418621419520 = -1 · 212 · 39 · 5 · 373	Discriminant
Eigenvalues	2+ 3- 5+ -2  2  3 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-18301,971339]	[a1,a2,a3,a4,a6]
Generators	[-103:1332:1]	Generators of the group modulo torsion
j	-165505319755264/4985014995	j-invariant
L	5.4472166813976	L(r)(E,1)/r!
Ω	0.68031388410951	Real period
R	0.1482762374031	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	17760t1 35520o1 53280ca1 88800bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17760l1

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
+	-	+	-2	2	3	-4	-4	6	1	-8	-	2	1	7	-13	-9	8	12	6	4	-8	-7	-9	-2

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Quadratic twists for elliptic curve 17760l1

-4	8	-3	5
17760t1	35520o1	53280ca1	88800bc1

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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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