Cremona's table of elliptic curves

2871 = 3² · 11 · 29

Field	Data	Notes
Atkin-Lehner	3- 11- 29+	Signs for the Atkin-Lehner involutions
Class	2871c	Isogeny class
Conductor	2871	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-12235126463109 = -1 · 320 · 112 · 29	Discriminant
Eigenvalues	-1 3-  2 -2 11-  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3119,-180372]	[a1,a2,a3,a4,a6]
Generators	[479:10155:1]	Generators of the group modulo torsion
j	-4601630708137/16783438221	j-invariant
L	2.3148536178923	L(r)(E,1)/r!
Ω	0.2927275733494	Real period
R	3.9539384544574	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45936bi2 957a2 71775be2 31581m2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2871c2

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

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Quadratic twists for elliptic curve 2871c2

-4	-3	5	-11	29
45936bi2	957a2	71775be2	31581m2	83259f2

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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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