Cremona's table of elliptic curves

4277 = 7 · 13 · 47

Field	Data	Notes
Atkin-Lehner	7- 13- 47+	Signs for the Atkin-Lehner involutions
Class	4277c	Isogeny class
Conductor	4277	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-460431881 = -1 · 73 · 134 · 47	Discriminant
Eigenvalues	-1 -3  1 7-  3 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-282,-2022]	[a1,a2,a3,a4,a6]
Generators	[22:34:1]	Generators of the group modulo torsion
j	-2471874619761/460431881	j-invariant
L	1.639651424444	L(r)(E,1)/r!
Ω	0.57684903211678	Real period
R	0.23686893987196	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	68432k1 38493i1 106925d1 29939b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4277c1

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
-1	-3	1	-	3	-	6	-4	-4	-2	-2	5	1	-5	+	-9	-11	12	12	-8	-15	0	-15	12	-2

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Quadratic twists for elliptic curve 4277c1

-4	-3	5	-7	13
68432k1	38493i1	106925d1	29939b1	55601b1

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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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