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	17760m	Isogeny class
Conductor	17760	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	2557440000 = 212 · 33 · 54 · 37	Discriminant
Eigenvalues	2+ 3- 5+ -4  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5361,-152865]	[a1,a2,a3,a4,a6]
Generators	[357:6600:1]	Generators of the group modulo torsion
j	4160851280704/624375	j-invariant
L	4.9469280865599	L(r)(E,1)/r!
Ω	0.55793712834075	Real period
R	2.9554871778424	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17760d3 35520bz1 53280cc4 88800be4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17760m2

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
+	-	+	-4	4	-2	-2	4	-8	2	0	-	10	4	0	-2	-4	-14	-4	8	2	0	12	6	-2

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Quadratic twists for elliptic curve 17760m2

-4	8	-3	5
17760d3	35520bz1	53280cc4	88800be4

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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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