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	2112o	Isogeny class
Conductor	2112	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-35684352 = -1 · 215 · 32 · 112	Discriminant
Eigenvalues	2+ 3-  4  2 11+ -4  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1,287]	[a1,a2,a3,a4,a6]
j	-8/1089	j-invariant
L	3.2852385303235	L(r)(E,1)/r!
Ω	1.6426192651617	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	2112i2 1056h2 6336bf2 52800m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112o2

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
+	-	4	2	+	-4	2	4	-6	6	-4	2	6	8	-10	12	0	-8	4	-6	10	6	-12	-14	-18

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Quadratic twists for elliptic curve 2112o2

-4	8	-3	5	-7	-11
2112i2	1056h2	6336bf2	52800m2	103488bk2	23232ck2

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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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