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	16	Product of Tamagawa factors cp
Δ	-13824849101488128 = -1 · 215 · 320 · 112	Discriminant
Eigenvalues	2+ 3+ -2  4 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-73569,9563553]	[a1,a2,a3,a4,a6]
j	-1343891598641864/421900912521	j-invariant
L	1.5009222044407	L(r)(E,1)/r!
Ω	0.37523055111017	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	2112n4 1056d4 6336n4 52800dh3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112h4

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 2112h4

-4	8	-3	5	-7	-11
2112n4	1056d4	6336n4	52800dh3	103488dx3	23232v3

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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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