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	2112v	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	77856768 = 218 · 33 · 11	Discriminant
Eigenvalues	2- 3+  2 -4 11-  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-417,3393]	[a1,a2,a3,a4,a6]
Generators	[-19:64:1]	Generators of the group modulo torsion
j	30664297/297	j-invariant
L	2.7231090972742	L(r)(E,1)/r!
Ω	1.9407488589349	Real period
R	1.4031228640107	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	2112l1 528h1 6336cc1 52800hf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112v1

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	-	2	-2	0	-8	6	8	-6	-2	0	-8	-6	-4	-6	-4	0	-14	4	12	-6	2

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Quadratic twists for elliptic curve 2112v1

-4	8	-3	5	-7	-11
2112l1	528h1	6336cc1	52800hf1	103488iu1	23232db1

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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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