Cremona's table of elliptic curves

89 = Prime conductor

Field	Data	Notes
Atkin-Lehner	89-	Signs for the Atkin-Lehner involutions
Conductor	89	Conductor
Count	2	Number of curves in isogeny class
Curves	89b1 89b2	Curves in isogeny class
deg	5	Modular degree for the optimal curve
Eigenvalues	1  2 -2  2 -4  2  6 -2	Hecke eigenvalues for primes less than 20
L	1.4223048292271	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	1424f 5696g 801b 2225b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 89b

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	-4	2	6	-2	2	-6	6	10	-6	2	12	-6	-10	-6	12	4	10	-12	-6	-	-18

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Quadratic twists for isogeny class 89b

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	89
1424f	5696g	801b	2225b	4361b	10769d	15041a	25721e	32129a	47081a	74849a	85529b	121841b	7921a

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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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