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	2736k	Isogeny class
Conductor	2736	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	6127239168 = 214 · 39 · 19	Discriminant
Eigenvalues	2- 3+  2  0 -2 -4  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-459,378]	[a1,a2,a3,a4,a6]
Generators	[-11:64:1]	Generators of the group modulo torsion
j	132651/76	j-invariant
L	3.5650381911473	L(r)(E,1)/r!
Ω	1.1487389207708	Real period
R	1.5517182044965	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	342d1 10944bn1 2736l1 68400dm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736k1

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	0	-2	-4	0	-	-8	-2	2	-8	-2	-4	4	2	0	-10	0	16	6	-14	6	-18	10

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Quadratic twists for elliptic curve 2736k1

-4	8	-3	5	-19
342d1	10944bn1	2736l1	68400dm1	51984bq1

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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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