Cremona's table of elliptic curves

5865 = 3 · 5 · 17 · 23

Field	Data	Notes
Atkin-Lehner	3+ 5- 17- 23+	Signs for the Atkin-Lehner involutions
Class	5865b	Isogeny class
Conductor	5865	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-3601843125 = -1 · 3 · 54 · 174 · 23	Discriminant
Eigenvalues	1 3+ 5-  0  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,218,2701]	[a1,a2,a3,a4,a6]
Generators	[2238:36451:8]	Generators of the group modulo torsion
j	1137566234519/3601843125	j-invariant
L	4.1855280014871	L(r)(E,1)/r!
Ω	0.99128694051741	Real period
R	4.2223173033051	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	93840cn3 17595m4 29325q3 99705o3	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5865b4

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	0	-2	-	4	+	-6	4	-2	6	-4	-8	14	-4	-6	4	8	10	-16	-8	-6	10

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Quadratic twists for elliptic curve 5865b4

-4	-3	5	17
93840cn3	17595m4	29325q3	99705o3

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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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