Cremona's table of elliptic curves

585 = 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 13-	Signs for the Atkin-Lehner involutions
Conductor	585	Conductor
Count	8	Number of curves in isogeny class
Curves	585f1 585f2 585f3 585f4 585f5 585f6 585f7 585f8	Curves in isogeny class
deg	192	Modular degree for the optimal curve
Eigenvalues	1 3- 5+  0 -4 13- -2 -4	Hecke eigenvalues for primes less than 20
L	2.3595617156492	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	9360bm 37440ca 195a 2925g	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 585f

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	-4	-	-2	-4	-8	2	-8	6	6	-4	8	-6	12	-2	-4	0	-6	16	4	-10	18

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Quadratic twists for isogeny class 585f

-4	8	-3	5	-7	-11	13
9360bm	37440ca	195a	2925g	28665bq	70785m	7605p

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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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