Cremona's table of elliptic curves

5871 = 3 · 19 · 103

Field	Data	Notes
Atkin-Lehner	3+ 19- 103+	Signs for the Atkin-Lehner involutions
Class	5871c	Isogeny class
Conductor	5871	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3984	Modular degree for the optimal curve
Δ	-146945259 = -1 · 36 · 19 · 1032	Discriminant
Eigenvalues	-2 3+ -1 -1 -1 -4 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-856,9948]	[a1,a2,a3,a4,a6]
Generators	[19:13:1] [24:51:1]	Generators of the group modulo torsion
j	-69446803492864/146945259	j-invariant
L	2.3111033978151	L(r)(E,1)/r!
Ω	1.8352667599072	Real period
R	0.31481845695438	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	93936i1 17613f1 111549e1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 5871c1

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	+	-1	-1	-1	-4	-5	-	-8	8	-8	4	-12	-11	-7	0	4	3	-2	4	-1	-2	0	2	-16

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Quadratic twists for elliptic curve 5871c1

-4	-3	-19
93936i1	17613f1	111549e1

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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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