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	2871d	Isogeny class
Conductor	2871	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1288	Modular degree for the optimal curve
Δ	-6743979 = -1 · 36 · 11 · 292	Discriminant
Eigenvalues	-2 3- -1  4 11-  6 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-333,2342]	[a1,a2,a3,a4,a6]
Generators	[13:14:1]	Generators of the group modulo torsion
j	-5601816576/9251	j-invariant
L	1.9264973873514	L(r)(E,1)/r!
Ω	2.3681542236825	Real period
R	0.40675082899705	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45936bh1 319a1 71775bl1 31581n1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2871d1

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	4	-	6	-4	-2	-3	+	-7	-11	-4	-4	-8	-2	3	2	-15	7	2	6	6	-9	-17

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Quadratic twists for elliptic curve 2871d1

-4	-3	5	-11	29
45936bh1	319a1	71775bl1	31581n1	83259h1

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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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