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	2112h	Isogeny class
Conductor	2112	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3541141131264 = 212 · 310 · 114	Discriminant
Eigenvalues	2+ 3+ -2  4 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-78409,8476489]	[a1,a2,a3,a4,a6]
j	13015685560572352/864536409	j-invariant
L	1.5009222044407	L(r)(E,1)/r!
Ω	0.75046110222034	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2112n2 1056d1 6336n2 52800dh2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112h2

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

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Quadratic twists for elliptic curve 2112h2

-4	8	-3	5	-7	-11
2112n2	1056d1	6336n2	52800dh2	103488dx2	23232v2

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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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