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	13944b	Isogeny class
Conductor	13944	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	12493824 = 210 · 3 · 72 · 83	Discriminant
Eigenvalues	2+ 3+ -2 7+ -6  6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-64,124]	[a1,a2,a3,a4,a6]
Generators	[-6:16:1]	Generators of the group modulo torsion
j	28756228/12201	j-invariant
L	2.8832795384918	L(r)(E,1)/r!
Ω	2.0323008836289	Real period
R	1.418726706128	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	27888m1 111552bl1 41832x1 97608k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13944b1

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	+	-6	6	-4	4	-4	4	-4	2	12	-10	12	2	-8	-10	6	-8	4	16	+	6	12

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Quadratic twists for elliptic curve 13944b1

-4	8	-3	-7
27888m1	111552bl1	41832x1	97608k1

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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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