Cremona's table of elliptic curves

2112 = 2⁶ · 3 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	2112x	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	66991423488 = 224 · 3 · 113	Discriminant
Eigenvalues	2- 3-  0 -2 11+  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5153,140127]	[a1,a2,a3,a4,a6]
Generators	[21:204:1]	Generators of the group modulo torsion
j	57736239625/255552	j-invariant
L	3.423589553502	L(r)(E,1)/r!
Ω	1.1055757199314	Real period
R	3.0966576886426	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	2112e3 528g3 6336ce3 52800eg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112x3

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
-	-	0	-2	+	4	-6	-4	-6	-6	-8	10	6	8	6	0	0	-8	-4	-6	2	-14	-12	-6	14

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Quadratic twists for elliptic curve 2112x3

-4	8	-3	5	-7	-11
2112e3	528g3	6336ce3	52800eg3	103488ff3	23232dm3

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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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