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	2736h	Isogeny class
Conductor	2736	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-4850731008 = -1 · 211 · 38 · 192	Discriminant
Eigenvalues	2+ 3- -4 -4 -4 -4 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,213,3130]	[a1,a2,a3,a4,a6]
Generators	[-7:36:1] [-1:54:1]	Generators of the group modulo torsion
j	715822/3249	j-invariant
L	3.1342938186768	L(r)(E,1)/r!
Ω	0.98104788167603	Real period
R	0.39935535731968	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1368j2 10944cr2 912d2 68400bs2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736h2

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

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Quadratic twists for elliptic curve 2736h2

-4	8	-3	5	-19
1368j2	10944cr2	912d2	68400bs2	51984bc2

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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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