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	2112r	Isogeny class
Conductor	2112	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1141899264 = 220 · 32 · 112	Discriminant
Eigenvalues	2+ 3- -2 -4 11-  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1409,-20769]	[a1,a2,a3,a4,a6]
Generators	[555:13056:1]	Generators of the group modulo torsion
j	1180932193/4356	j-invariant
L	3.0643337311967	L(r)(E,1)/r!
Ω	0.77936781222215	Real period
R	3.9318197173932	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2112u2 66b2 6336o2 52800bj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112r2

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

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Quadratic twists for elliptic curve 2112r2

-4	8	-3	5	-7	-11
2112u2	66b2	6336o2	52800bj2	103488by2	23232cg2

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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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