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	2728c	Isogeny class
Conductor	2728	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	-57675376 = -1 · 24 · 112 · 313	Discriminant
Eigenvalues	2+  0 -3 -5 11+ -6  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-119,619]	[a1,a2,a3,a4,a6]
Generators	[-9:31:1] [-5:33:1]	Generators of the group modulo torsion
j	-11647819008/3604711	j-invariant
L	3.1654991511882	L(r)(E,1)/r!
Ω	1.8741137687873	Real period
R	0.14075538012992	Regulator
r	2	Rank of the group of rational points
S	0.99999999999989	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5456b1 21824l1 24552x1 68200t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2728c1

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	-3	-5	+	-6	0	-5	-2	-2	-	8	-11	6	-8	2	-1	-14	-8	3	-2	-10	4	-6	17

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Quadratic twists for elliptic curve 2728c1

-4	8	-3	5	-11	-31
5456b1	21824l1	24552x1	68200t1	30008h1	84568c1

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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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