Cremona's table of elliptic curves

289 = 17²

Field	Data	Notes
Atkin-Lehner	17+	Signs for the Atkin-Lehner involutions
Conductor	289	Conductor
Count	4	Number of curves in isogeny class
Curves	289a1 289a2 289a3 289a4	Curves in isogeny class
deg	72	Modular degree for the optimal curve
Eigenvalues	-1  0  2 -4  0 -2 17+ -4	Hecke eigenvalues for primes less than 20
L	1.1388947569598	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	4624e 18496c 2601j 7225b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 289a

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 isogeny class 289a

-4	8	-3	5	-7	-11	13	17	-19
4624e	18496c	2601j	7225b	14161b	34969e	48841a	17a	104329d

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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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