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	14112bi	Isogeny class
Conductor	14112	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-488117230272 = -1 · 26 · 33 · 710	Discriminant
Eigenvalues	2- 3+  0 7- -4 -2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2205,-52136]	[a1,a2,a3,a4,a6]
Generators	[231:3430:1]	Generators of the group modulo torsion
j	-5832000/2401	j-invariant
L	4.4615053857074	L(r)(E,1)/r!
Ω	0.34145193230196	Real period
R	3.2665691446153	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	14112bh1 28224dl2 14112c1 2016j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 14112bi1

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	-	-4	-2	4	0	-4	4	8	-2	-4	8	8	-4	8	2	8	-12	-6	-8	16	-12	2

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Quadratic twists for elliptic curve 14112bi1

-4	8	-3	-7
14112bh1	28224dl2	14112c1	2016j1

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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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