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	4257a	Isogeny class
Conductor	4257	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-5283042416091 = -1 · 33 · 113 · 435	Discriminant
Eigenvalues	-1 3+  1  3 11+ -2 -3  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1412,-112102]	[a1,a2,a3,a4,a6]
Generators	[72:358:1]	Generators of the group modulo torsion
j	-11523267816003/195668237633	j-invariant
L	2.7057456921605	L(r)(E,1)/r!
Ω	0.32850501525119	Real period
R	4.1182715126762	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	68112bj1 4257c1 106425c1 46827f1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4257a1

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	+	-2	-3	4	4	-6	-1	-6	-5	+	2	-10	-6	-1	3	-5	-7	10	-3	-5	7

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Quadratic twists for elliptic curve 4257a1

-4	-3	5	-11
68112bj1	4257c1	106425c1	46827f1

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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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