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
deg	2240	Modular degree for the optimal curve
Δ	14749082073 = 313 · 11 · 292	Discriminant
Eigenvalues	-1 3-  2 -2 11-  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4424,-111990]	[a1,a2,a3,a4,a6]
Generators	[110:795:1]	Generators of the group modulo torsion
j	13132563308857/20231937	j-invariant
L	2.3148536178923	L(r)(E,1)/r!
Ω	0.58545514669879	Real period
R	1.9769692272287	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	45936bi1 957a1 71775be1 31581m1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2871c1

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 2871c1

-4	-3	5	-11	29
45936bi1	957a1	71775be1	31581m1	83259f1

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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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