Cremona's table of elliptic curves

8514 = 2 · 3² · 11 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 43+	Signs for the Atkin-Lehner involutions
Class	8514d	Isogeny class
Conductor	8514	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	425617623306087696 = 24 · 312 · 114 · 434	Discriminant
Eigenvalues	2+ 3-  2  0 11- -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-601821,177088437]	[a1,a2,a3,a4,a6]
Generators	[-126:15903:1]	Generators of the group modulo torsion
j	33067289963089830097/583837617703824	j-invariant
L	3.7223854052182	L(r)(E,1)/r!
Ω	0.29852713737144	Real period
R	3.1172923155279	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	68112bu4 2838e3 93654bp4	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 8514d3

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	0	-	-2	6	-4	0	2	0	-10	-2	+	-8	-6	-4	-2	4	8	-6	-8	4	-2	2

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Quadratic twists for elliptic curve 8514d3

-4	-3	-11
68112bu4	2838e3	93654bp4

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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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