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	2736m	Isogeny class
Conductor	2736	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-10486202499072 = -1 · 221 · 36 · 193	Discriminant
Eigenvalues	2- 3-  0  1 -6  5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1365,154586]	[a1,a2,a3,a4,a6]
Generators	[-43:128:1]	Generators of the group modulo torsion
j	94196375/3511808	j-invariant
L	3.3034068917671	L(r)(E,1)/r!
Ω	0.54577851344788	Real period
R	1.5131627621699	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	342a2 10944cf2 304b2 68400ee2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736m2

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
-	-	0	1	-6	5	-3	+	3	-9	4	2	0	-8	0	3	9	-10	-5	-6	-7	10	-6	12	-10

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Quadratic twists for elliptic curve 2736m2

-4	8	-3	5	-19
342a2	10944cf2	304b2	68400ee2	51984ci2

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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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