Cremona's table of elliptic curves

13944 = 2³ · 3 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 83+	Signs for the Atkin-Lehner involutions
Class	13944k	Isogeny class
Conductor	13944	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5440	Modular degree for the optimal curve
Δ	187491024 = 24 · 35 · 7 · 832	Discriminant
Eigenvalues	2- 3+ -2 7-  4  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-539,-4596]	[a1,a2,a3,a4,a6]
Generators	[69:531:1]	Generators of the group modulo torsion
j	1084365064192/11718189	j-invariant
L	4.0255577808934	L(r)(E,1)/r!
Ω	0.99133120594546	Real period
R	4.0607596701792	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	27888i1 111552bu1 41832l1 97608x1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13944k1

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	2	-2	4	2	-4	-2	-10	-12	12	-12	-4	2	-8	-6	4	-12	+	-2	8

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Quadratic twists for elliptic curve 13944k1

-4	8	-3	-7
27888i1	111552bu1	41832l1	97608x1

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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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