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	2736p	Isogeny class
Conductor	2736	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-31912704 = -1 · 28 · 38 · 19	Discriminant
Eigenvalues	2- 3-  3 -1 -5 -6  5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,268]	[a1,a2,a3,a4,a6]
Generators	[2:18:1]	Generators of the group modulo torsion
j	8192/171	j-invariant
L	3.6033257408913	L(r)(E,1)/r!
Ω	1.5560191403515	Real period
R	0.57893338961069	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	684c1 10944cp1 912i1 68400dz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736p1

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	-5	-6	5	+	4	-6	-6	-8	8	-9	1	-2	-8	11	0	-4	-11	8	-4	-10	-10

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Quadratic twists for elliptic curve 2736p1

-4	8	-3	5	-19
684c1	10944cp1	912i1	68400dz1	51984cu1

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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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