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	2080a	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]
Generators	[11:6:1]	Generators of the group modulo torsion
j	140283769536/325	j-invariant
L	2.9675442339645	L(r)(E,1)/r!
Ω	3.3119365300993	Real period
R	0.89601482606779	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	2080b1 4160e2 18720bl1 10400v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2080a1

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 2080a1

-4	8	-3	5	-7	13
2080b1	4160e2	18720bl1	10400v1	101920s1	27040s1

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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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