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	5871b	Isogeny class
Conductor	5871	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-362422701 = -1 · 33 · 194 · 103	Discriminant
Eigenvalues	-1 3+ -3 -2 -6 -1  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1217,15860]	[a1,a2,a3,a4,a6]
Generators	[-22:191:1] [16:20:1]	Generators of the group modulo torsion
j	-199350693197713/362422701	j-invariant
L	2.461884900608	L(r)(E,1)/r!
Ω	1.7003967877522	Real period
R	0.36195741463691	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	93936k1 17613d1 111549d1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 5871b1

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	+	-3	-2	-6	-1	4	-	9	-6	-5	2	-8	-9	2	-10	-15	-13	-3	-8	-4	-10	17	-2	-11

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Quadratic twists for elliptic curve 5871b1

-4	-3	-19
93936k1	17613d1	111549d1

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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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