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	2196b	Isogeny class
Conductor	2196	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-1607472 = -1 · 24 · 33 · 612	Discriminant
Eigenvalues	2- 3+  0  0 -2 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-60,189]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	-55296000/3721	j-invariant
L	3.0649289937595	L(r)(E,1)/r!
Ω	2.6256024361585	Real period
R	1.1673240973389	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	8784k1 35136a1 2196a1 54900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2196b1

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

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Quadratic twists for elliptic curve 2196b1

-4	8	-3	5	-7
8784k1	35136a1	2196a1	54900b1	107604d1

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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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