Cremona's table of elliptic curves

2736 = 2⁴ · 3² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	2736q	Isogeny class
Conductor	2736	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-56733696 = -1 · 212 · 36 · 19	Discriminant
Eigenvalues	2- 3- -3  1  3 -4  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,96,-16]	[a1,a2,a3,a4,a6]
Generators	[1:9:1]	Generators of the group modulo torsion
j	32768/19	j-invariant
L	2.8856369743314	L(r)(E,1)/r!
Ω	1.177586472244	Real period
R	1.2252335783174	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	171b1 10944cn1 304e1 68400ec1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736q1

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	1	3	-4	3	+	0	-6	4	2	6	1	-3	-12	-6	-1	4	6	-7	-8	12	-12	8

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Quadratic twists for elliptic curve 2736q1

-4	8	-3	5	-19
171b1	10944cn1	304e1	68400ec1	51984cw1

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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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