Cremona's table of elliptic curves

2080 = 2⁵ · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	2080d	Isogeny class
Conductor	2080	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-17305600 = -1 · 212 · 52 · 132	Discriminant
Eigenvalues	2- -2 5+ -4 -6 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-81,319]	[a1,a2,a3,a4,a6]
Generators	[-6:25:1] [-1:20:1]	Generators of the group modulo torsion
j	-14526784/4225	j-invariant
L	2.4786322970595	L(r)(E,1)/r!
Ω	2.0758194073194	Real period
R	0.29851251610788	Regulator
r	2	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2080c2 4160r1 18720v2 10400k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2080d2

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

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Quadratic twists for elliptic curve 2080d2

-4	8	-3	5	-7	13
2080c2	4160r1	18720v2	10400k2	101920bs2	27040l2

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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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