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	5865f	Isogeny class
Conductor	5865	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	54984375 = 32 · 56 · 17 · 23	Discriminant
Eigenvalues	1 3- 5- -2 -6 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2078,-36619]	[a1,a2,a3,a4,a6]
j	991653330582361/54984375	j-invariant
L	2.1214651769409	L(r)(E,1)/r!
Ω	0.70715505898029	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	93840bu2 17595n2 29325e2 99705a2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5865f2

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	-	-	-2	-6	-2	-	4	+	4	0	2	-8	8	8	6	10	-2	8	12	-4	-4	-12	8	6

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Quadratic twists for elliptic curve 5865f2

-4	-3	5	17
93840bu2	17595n2	29325e2	99705a2

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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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