Cremona's table of elliptic curves

2136 = 2³ · 3 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 89-	Signs for the Atkin-Lehner involutions
Class	2136a	Isogeny class
Conductor	2136	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	7846211930112 = 211 · 316 · 89	Discriminant
Eigenvalues	2- 3- -2  4 -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5984,-118560]	[a1,a2,a3,a4,a6]
j	11572870364354/3831158169	j-invariant
L	2.2288478934612	L(r)(E,1)/r!
Ω	0.55721197336531	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	4272a3 17088b3 6408a3 53400e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2136a3

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	-4	2	2	4	4	-6	4	2	2	4	0	6	4	2	4	8	-6	0	-4	-	18

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Quadratic twists for elliptic curve 2136a3

-4	8	-3	5	-7
4272a3	17088b3	6408a3	53400e4	104664g4

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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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