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	34398225 = 32 · 52 · 172 · 232	Discriminant
Eigenvalues	1 3+ 5-  0  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-127,424]	[a1,a2,a3,a4,a6]
Generators	[-12:26:1]	Generators of the group modulo torsion
j	229333309561/34398225	j-invariant
L	4.1855280014871	L(r)(E,1)/r!
Ω	1.9825738810348	Real period
R	2.1111586516526	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	93840cn2 17595m2 29325q2 99705o2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5865b2

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 5865b2

-4	-3	5	17
93840cn2	17595m2	29325q2	99705o2

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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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