Cremona's table of elliptic curves

3286 = 2 · 31 · 53

Field	Data	Notes
Atkin-Lehner	2+ 31+ 53-	Signs for the Atkin-Lehner involutions
Class	3286c	Isogeny class
Conductor	3286	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-13038848 = -1 · 28 · 312 · 53	Discriminant
Eigenvalues	2+ -3 -2 -2  0 -5 -1  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-28,-176]	[a1,a2,a3,a4,a6]
Generators	[8:4:1] [9:11:1]	Generators of the group modulo torsion
j	-2476813977/13038848	j-invariant
L	1.9473788004205	L(r)(E,1)/r!
Ω	0.93290010925182	Real period
R	0.52186155331856	Regulator
r	2	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26288j1 105152c1 29574i1 82150h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3286c1

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
+	-3	-2	-2	0	-5	-1	1	-5	3	+	-9	0	0	-12	-	-10	6	-4	-13	-10	-5	-9	-10	-7

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Quadratic twists for elliptic curve 3286c1

-4	8	-3	5	-31
26288j1	105152c1	29574i1	82150h1	101866e1

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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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