Cremona's table of elliptic curves

28392 = 2³ · 3 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	28392a	Isogeny class
Conductor	28392	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48384	Modular degree for the optimal curve
Δ	-24288193972224 = -1 · 211 · 33 · 7 · 137	Discriminant
Eigenvalues	2+ 3+ -1 7+ -5 13+  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-56,237132]	[a1,a2,a3,a4,a6]
Generators	[61:676:1]	Generators of the group modulo torsion
j	-2/2457	j-invariant
L	3.350520521415	L(r)(E,1)/r!
Ω	0.53549304616651	Real period
R	1.5642222365914	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56784r1 85176br1 2184i1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 28392a1

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
+	+	-1	+	-5	+	3	-1	3	-3	0	3	0	7	0	-2	8	-5	-10	0	-9	14	-6	2	2

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Quadratic twists for elliptic curve 28392a1

-4	-3	13
56784r1	85176br1	2184i1

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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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