Cremona's table of elliptic curves

689 = 13 · 53

Field	Data	Notes
Atkin-Lehner	13+ 53+	Signs for the Atkin-Lehner involutions
Conductor	689	Conductor
Count	2	Number of curves in isogeny class
Curves	689a1 689a2	Curves in isogeny class
deg	40	Modular degree for the optimal curve
Eigenvalues	-1 -2 -2  2  2 13+ -2  4	Hecke eigenvalues for primes less than 20
L	1.033304817561	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	11024f 44096j 6201d 17225e	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 689a

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	-2	-2	2	2	+	-2	4	6	6	-8	-6	-10	-12	6	+	-6	10	-8	-12	14	-10	12	10	-14

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Quadratic twists for isogeny class 689a

-4	8	-3	5	-7	-11	13	53
11024f	44096j	6201d	17225e	33761c	83369f	8957a	36517a

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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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