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	6975757441 = 178	Discriminant
Eigenvalues	-1  0  2 -4  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1644,-24922]	[a1,a2,a3,a4,a6]
Generators	[-2945:3594:125]	Generators of the group modulo torsion
j	20346417/289	j-invariant
L	1.1388947569598	L(r)(E,1)/r!
Ω	0.75044391001715	Real period
R	6.0705123554607	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4624e2 18496c2 2601j2 7225b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 289a2

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 289a2

-4	8	-3	5	-7	-11	13	17	-19
4624e2	18496c2	2601j2	7225b2	14161b2	34969e2	48841a2	17a2	104329d2

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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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