Cremona's table of elliptic curves

4557 = 3 · 7² · 31

Field	Data	Notes
Atkin-Lehner	3- 7- 31+	Signs for the Atkin-Lehner involutions
Class	4557k	Isogeny class
Conductor	4557	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	26699463 = 34 · 73 · 312	Discriminant
Eigenvalues	-1 3-  0 7-  2 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-78,-99]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	153130375/77841	j-invariant
L	2.876840564776	L(r)(E,1)/r!
Ω	1.6954345554291	Real period
R	0.42420401241143	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	72912bm2 13671k2 113925n2 4557d2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4557k2

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	-	0	-	2	-2	-2	4	-2	-2	+	-10	-4	10	-4	-6	0	14	-8	4	-14	10	12	-18	-12

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Quadratic twists for elliptic curve 4557k2

-4	-3	5	-7
72912bm2	13671k2	113925n2	4557d2

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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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