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	2112f	Isogeny class
Conductor	2112	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2364899328 = 215 · 38 · 11	Discriminant
Eigenvalues	2+ 3+  2  0 11-  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-577,-4607]	[a1,a2,a3,a4,a6]
j	649461896/72171	j-invariant
L	1.9619904636908	L(r)(E,1)/r!
Ω	0.98099523184538	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2112k3 1056i2 6336p3 52800cr4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112f3

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	0	-	6	2	4	-4	-2	-4	2	10	4	-4	-6	12	6	4	-4	10	-16	-4	10	2

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Quadratic twists for elliptic curve 2112f3

-4	8	-3	5	-7	-11
2112k3	1056i2	6336p3	52800cr4	103488ef4	23232n4

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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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