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	2080b	Isogeny class
Conductor	2080	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	20800 = 26 · 52 · 13	Discriminant
Eigenvalues	2-  0 5+ -2 -2 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-433,-3468]	[a1,a2,a3,a4,a6]
j	140283769536/325	j-invariant
L	1.0465925548175	L(r)(E,1)/r!
Ω	1.0465925548175	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2080a1 4160f2 18720t1 10400f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2080b1

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	+	-2	-2	+	-2	2	4	2	6	2	2	4	6	6	14	6	-10	-2	-14	4	14	-14	-6

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Quadratic twists for elliptic curve 2080b1

-4	8	-3	5	-7	13
2080a1	4160f2	18720t1	10400f1	101920bq1	27040i1

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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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