Cremona's table of elliptic curves

8993 = 17 · 23²

Field	Data	Notes
Atkin-Lehner	17+ 23-	Signs for the Atkin-Lehner involutions
Conductor	8993	Conductor
Count	4	Number of curves in isogeny class
Curves	8993a1 8993a2 8993a3 8993a4	Curves in isogeny class
deg	3080	Modular degree for the optimal curve
Eigenvalues	-1  0  2 -4  0 -2 17+  4	Hecke eigenvalues for primes less than 20
L	0.57252618336207	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	80937s 17a	Quadratic twists by: -3 -23

Hecke Eigenvalues for isogeny class 8993a

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	-	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 8993a

-3	-23
80937s	17a

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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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