Cremona's table of elliptic curves

4257 = 3² · 11 · 43

Field	Data	Notes
Atkin-Lehner	3+ 11- 43-	Signs for the Atkin-Lehner involutions
Class	4257d	Isogeny class
Conductor	4257	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-12771 = -1 · 33 · 11 · 43	Discriminant
Eigenvalues	-1 3+ -3  5 11- -6  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1,-6]	[a1,a2,a3,a4,a6]
Generators	[2:0:1]	Generators of the group modulo torsion
j	9261/473	j-invariant
L	2.188652045022	L(r)(E,1)/r!
Ω	1.9115079260643	Real period
R	0.57249358351557	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	68112bd1 4257b1 106425e1 46827a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4257d1

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	5	-	-6	3	4	-4	-6	-5	6	-3	-	-10	-2	2	13	7	3	-5	6	7	-17	-9

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Quadratic twists for elliptic curve 4257d1

-4	-3	5	-11
68112bd1	4257b1	106425e1	46827a1

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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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