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	4257c	Isogeny class
Conductor	4257	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-3851337921330339 = -1 · 39 · 113 · 435	Discriminant
Eigenvalues	1 3+ -1  3 11- -2  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12705,3039452]	[a1,a2,a3,a4,a6]
j	-11523267816003/195668237633	j-invariant
L	2.2340784372302	L(r)(E,1)/r!
Ω	0.37234640620503	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	68112be1 4257a1 106425f1 46827h1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4257c1

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 4257c1

-4	-3	5	-11
68112be1	4257a1	106425f1	46827h1

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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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