Cremona's table of elliptic curves

2728 = 2³ · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 11+ 31+	Signs for the Atkin-Lehner involutions
Class	2728a	Isogeny class
Conductor	2728	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-698368 = -1 · 211 · 11 · 31	Discriminant
Eigenvalues	2+  2  0 -3 11+  0 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,44]	[a1,a2,a3,a4,a6]
Generators	[1:6:1]	Generators of the group modulo torsion
j	-31250/341	j-invariant
L	4.0869110229074	L(r)(E,1)/r!
Ω	2.4357626476761	Real period
R	1.6778773690477	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5456d1 21824h1 24552p1 68200r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2728a1

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	0	-3	+	0	-3	2	-1	10	+	-5	-12	-1	-2	-10	11	4	-3	-12	-14	6	-9	0	1

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Quadratic twists for elliptic curve 2728a1

-4	8	-3	5	-11	-31
5456d1	21824h1	24552p1	68200r1	30008e1	84568f1

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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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