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	2112u	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]
j	4824238966273/66	j-invariant
L	1.5514344999618	L(r)(E,1)/r!
Ω	1.5514344999618	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2112r3 528j3 6336ci3 52800gp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112u3

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 2112u3

-4	8	-3	5	-7	-11
2112r3	528j3	6336ci3	52800gp4	103488ht4	23232de4

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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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