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	2196d	Isogeny class
Conductor	2196	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	57631824 = 24 · 310 · 61	Discriminant
Eigenvalues	2- 3- -2  2 -2 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156,-655]	[a1,a2,a3,a4,a6]
Generators	[-8:9:1]	Generators of the group modulo torsion
j	35995648/4941	j-invariant
L	2.8977255352643	L(r)(E,1)/r!
Ω	1.3631832382352	Real period
R	0.70856836018999	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	8784s1 35136x1 732a1 54900l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2196d1

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

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Quadratic twists for elliptic curve 2196d1

-4	8	-3	5	-7
8784s1	35136x1	732a1	54900l1	107604x1

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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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