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	2080f	Isogeny class
Conductor	2080	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	6760000 = 26 · 54 · 132	Discriminant
Eigenvalues	2-  0 5- -4 -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-217,-1224]	[a1,a2,a3,a4,a6]
j	17657244864/105625	j-invariant
L	1.244345813167	L(r)(E,1)/r!
Ω	1.244345813167	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2080e1 4160l2 18720m1 10400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2080f1

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

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Quadratic twists for elliptic curve 2080f1

-4	8	-3	5	-7	13
2080e1	4160l2	18720m1	10400a1	101920w1	27040b1

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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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