Cremona's table of elliptic curves

2196 = 2² · 3² · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 61-	Signs for the Atkin-Lehner involutions
Class	2196f	Isogeny class
Conductor	2196	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-11384064 = -1 · 28 · 36 · 61	Discriminant
Eigenvalues	2- 3-  3 -3  1  1  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,9,-162]	[a1,a2,a3,a4,a6]
j	432/61	j-invariant
L	2.1442627082389	L(r)(E,1)/r!
Ω	1.0721313541195	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8784z1 35136s1 244a1 54900s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2196f1

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
-	-	3	-3	1	1	2	2	-3	8	0	-2	3	8	4	10	-9	-	13	12	5	-17	-12	8	-18

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Quadratic twists for elliptic curve 2196f1

-4	8	-3	5	-7
8784z1	35136s1	244a1	54900s1	107604s1

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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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