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	5865g	Isogeny class
Conductor	5865	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-339478121193135 = -1 · 3 · 5 · 172 · 238	Discriminant
Eigenvalues	-1 3- 5-  0 -4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,17290,143187]	[a1,a2,a3,a4,a6]
j	571619613636358559/339478121193135	j-invariant
L	1.3185646262779	L(r)(E,1)/r!
Ω	0.32964115656947	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	93840bs5 17595k6 29325a5 99705b5	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5865g6

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	-4	-2	-	4	+	6	-8	6	2	4	-8	6	4	-2	-4	0	2	8	12	-14	2

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Quadratic twists for elliptic curve 5865g6

-4	-3	5	17
93840bs5	17595k6	29325a5	99705b5

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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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