Cremona's table of elliptic curves

289 = 17²

Field	Data	Notes
Atkin-Lehner	17+	Signs for the Atkin-Lehner involutions
Class	289a	Isogeny class
Conductor	289	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	410338673 = 177	Discriminant
Eigenvalues	-1  0  2 -4  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-26209,-1626560]	[a1,a2,a3,a4,a6]
Generators	[625:14715:1]	Generators of the group modulo torsion
j	82483294977/17	j-invariant
L	1.1388947569598	L(r)(E,1)/r!
Ω	0.37522195500858	Real period
R	3.0352561777303	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	4624e3 18496c3 2601j3 7225b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 289a3

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	-4	0	-2	+	-4	-4	-6	-4	2	6	4	0	6	-12	10	4	4	6	-12	-4	10	-2

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Quadratic twists for elliptic curve 289a3

-4	8	-3	5	-7	-11	13	17	-19
4624e3	18496c3	2601j3	7225b3	14161b3	34969e4	48841a4	17a3	104329d4

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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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