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	4277b	Isogeny class
Conductor	4277	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-55601 = -1 · 7 · 132 · 47	Discriminant
Eigenvalues	-1  1 -3 7- -1 13+  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-7,-14]	[a1,a2,a3,a4,a6]
Generators	[6:10:1]	Generators of the group modulo torsion
j	-38272753/55601	j-invariant
L	2.1683937727107	L(r)(E,1)/r!
Ω	1.3936122316894	Real period
R	0.7779760120511	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	68432f1 38493e1 106925e1 29939d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4277b1

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	1	-3	-	-1	+	4	0	0	0	10	-9	1	9	-	3	7	-10	0	12	-7	0	-5	10	-12

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Quadratic twists for elliptic curve 4277b1

-4	-3	5	-7	13
68432f1	38493e1	106925e1	29939d1	55601a1

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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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