Cremona's table of elliptic curves

2747 = 41 · 67

Field	Data	Notes
Atkin-Lehner	41- 67+	Signs for the Atkin-Lehner involutions
Class	2747a	Isogeny class
Conductor	2747	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	308	Modular degree for the optimal curve
Δ	-112627 = -1 · 412 · 67	Discriminant
Eigenvalues	0  2  4 -2  2  0  5  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1,-16]	[a1,a2,a3,a4,a6]
j	-262144/112627	j-invariant
L	2.9898667204208	L(r)(E,1)/r!
Ω	1.4949333602104	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	43952d1 24723a1 68675b1 112627c1	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 2747a1

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	2	4	-2	2	0	5	1	-7	9	4	-9	-	4	9	0	5	4	+	0	1	6	-12	1	16

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Quadratic twists for elliptic curve 2747a1

-4	-3	5	41
43952d1	24723a1	68675b1	112627c1

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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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