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	16	Product of Tamagawa factors cp
Δ	-122388124222881792 = -1 · 219 · 32 · 1110	Discriminant
Eigenvalues	2+ 3+  4 -2 11+ -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-643521,-199194687]	[a1,a2,a3,a4,a6]
Generators	[419111:9925280:343]	Generators of the group modulo torsion
j	-112427521449300721/466873642818	j-invariant
L	3.0564945320705	L(r)(E,1)/r!
Ω	0.084259891668195	Real period
R	9.068651975327	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	2112bd4 66c4 6336bg4 52800ce4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112d4

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 2112d4

-4	8	-3	5	-7	-11
2112bd4	66c4	6336bg4	52800ce4	103488do4	23232ba4

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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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