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	4	Product of Tamagawa factors cp
Δ	17301504 = 219 · 3 · 11	Discriminant
Eigenvalues	2+ 3- -2 -4 11-  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-22529,-1309089]	[a1,a2,a3,a4,a6]
Generators	[4506:102765:8]	Generators of the group modulo torsion
j	4824238966273/66	j-invariant
L	3.0643337311967	L(r)(E,1)/r!
Ω	0.38968390611107	Real period
R	7.8636394347865	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	2112u3 66b3 6336o3 52800bj4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112r3

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 2112r3

-4	8	-3	5	-7	-11
2112u3	66b3	6336o3	52800bj4	103488by4	23232cg4

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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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