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
deg	72	Modular degree for the optimal curve
Δ	410338673 = 177	Discriminant
Eigenvalues	-1  0  2 -4  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-199,510]	[a1,a2,a3,a4,a6]
Generators	[-12:38:1]	Generators of the group modulo torsion
j	35937/17	j-invariant
L	1.1388947569598	L(r)(E,1)/r!
Ω	1.5008878200343	Real period
R	3.0352561777303	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	4624e1 18496c1 2601j1 7225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 289a1

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 289a1

-4	8	-3	5	-7	-11	13	17	-19
4624e1	18496c1	2601j1	7225b1	14161b1	34969e1	48841a1	17a4	104329d1

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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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