Cremona's table of elliptic curves

8944 = 2⁴ · 13 · 43

Field	Data	Notes
Atkin-Lehner	2- 13- 43+	Signs for the Atkin-Lehner involutions
Class	8944d	Isogeny class
Conductor	8944	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3744	Modular degree for the optimal curve
Δ	-1172307968 = -1 · 221 · 13 · 43	Discriminant
Eigenvalues	2- -1  0  1 -3 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1248,-16640]	[a1,a2,a3,a4,a6]
Generators	[144:1664:1]	Generators of the group modulo torsion
j	-52523718625/286208	j-invariant
L	3.4598062274466	L(r)(E,1)/r!
Ω	0.40146289598141	Real period
R	2.1544993709748	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1118a1 35776g1 80496bn1 116272m1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8944d1

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
-	-1	0	1	-3	-	6	-2	-9	9	4	2	6	+	6	-6	3	-10	4	12	-7	-8	12	3	8

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Quadratic twists for elliptic curve 8944d1

-4	8	-3	13
1118a1	35776g1	80496bn1	116272m1

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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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