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	2736c	Isogeny class
Conductor	2736	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-155952 = -1 · 24 · 33 · 192	Discriminant
Eigenvalues	2+ 3+  4  0  6  2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-18,35]	[a1,a2,a3,a4,a6]
j	-1492992/361	j-invariant
L	3.0904696922437	L(r)(E,1)/r!
Ω	3.0904696922437	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1368d1 10944bp1 2736d1 68400e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736c1

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	0	6	2	4	-	-6	10	-8	-10	-6	4	-6	2	-4	10	12	-12	-6	4	-14	-6	-2

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Quadratic twists for elliptic curve 2736c1

-4	8	-3	5	-19
1368d1	10944bp1	2736d1	68400e1	51984g1

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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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