Cremona's table of elliptic curves

14112 = 2⁵ · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	14112bn	Isogeny class
Conductor	14112	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-148203857088 = -1 · 26 · 39 · 76	Discriminant
Eigenvalues	2- 3+ -4 7-  0  6 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1323,0]	[a1,a2,a3,a4,a6]
Generators	[7:98:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	3.4302001796144	L(r)(E,1)/r!
Ω	0.61484728129084	Real period
R	1.3947366622541	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	14112bn1 28224eg2 14112i1 288e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 14112bn1

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
-	+	-4	-	0	6	-8	0	0	-4	0	-2	8	0	0	-4	0	10	0	0	-6	0	0	-16	18

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Quadratic twists for elliptic curve 14112bn1

-4	8	-3	-7
14112bn1	28224eg2	14112i1	288e1

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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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