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	2112w	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	540672 = 214 · 3 · 11	Discriminant
Eigenvalues	2- 3+ -2  0 11- -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49,145]	[a1,a2,a3,a4,a6]
Generators	[-3:16:1]	Generators of the group modulo torsion
j	810448/33	j-invariant
L	2.3845318590158	L(r)(E,1)/r!
Ω	2.8965863504237	Real period
R	0.82322139599497	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	2112m1 528d1 6336bz1 52800gr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112w1

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	-	-2	6	0	-4	-2	0	10	6	-8	4	6	-12	-2	4	-12	-14	-16	-12	10	-14

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Quadratic twists for elliptic curve 2112w1

-4	8	-3	5	-7	-11
2112m1	528d1	6336bz1	52800gr1	103488in1	23232dc1

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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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