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	2112d	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	506622640128 = 220 · 3 · 115	Discriminant
Eigenvalues	2+ 3+  4 -2 11+ -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-644161,-198779327]	[a1,a2,a3,a4,a6]
Generators	[409514276955:-16170174629888:210644875]	Generators of the group modulo torsion
j	112763292123580561/1932612	j-invariant
L	3.0564945320705	L(r)(E,1)/r!
Ω	0.16851978333639	Real period
R	18.137303950654	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	2112bd3 66c3 6336bg3 52800ce3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112d3

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

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Quadratic twists for elliptic curve 2112d3

-4	8	-3	5	-7	-11
2112bd3	66c3	6336bg3	52800ce3	103488do3	23232ba3

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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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