Cremona's table of elliptic curves

160 = 2⁵ · 5

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	160a	Isogeny class
Conductor	160	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	320 = 26 · 5	Discriminant
Eigenvalues	2+ -2 5+ -2 -4 -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	438976/5	j-invariant
L	0.9777440810458	L(r)(E,1)/r!
Ω	5.4517057363795	Real period
R	0.35869290395528	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	160b1 320d2 1440m1 800g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 160a1

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

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Quadratic twists for elliptic curve 160a1

-4	8	-3	5	-7	-11	13	17	-19	-23
160b1	320d2	1440m1	800g1	7840n1	19360u1	27040u1	46240j1	57760j1	84640i1

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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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