Cremona's table of elliptic curves

14240 = 2⁵ · 5 · 89

Field	Data	Notes
Atkin-Lehner	2+ 5+ 89-	Signs for the Atkin-Lehner involutions
Class	14240f	Isogeny class
Conductor	14240	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2816	Modular degree for the optimal curve
Δ	3560000 = 26 · 54 · 89	Discriminant
Eigenvalues	2+  2 5+ -4  4  4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-46,96]	[a1,a2,a3,a4,a6]
j	171879616/55625	j-invariant
L	2.306341688896	L(r)(E,1)/r!
Ω	2.306341688896	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14240g1 28480bu1 128160bi1 71200r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 14240f1

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

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Quadratic twists for elliptic curve 14240f1

-4	8	-3	5
14240g1	28480bu1	128160bi1	71200r1

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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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