Cremona's table of elliptic curves

578 = 2 · 17²

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Conductor	578	Conductor
Count	4	Number of curves in isogeny class
Curves	578a1 578a2 578a3 578a4	Curves in isogeny class
deg	576	Modular degree for the optimal curve
Eigenvalues	2-  2  0  4 -6  2 17+ -4	Hecke eigenvalues for primes less than 20
L	3.2710755444012	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	4624f 18496g 5202a 14450g	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 578a

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
-	2	0	4	-6	2	+	-4	0	0	4	4	-6	8	0	-6	0	4	8	0	-2	-8	0	-6	-14

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Quadratic twists for isogeny class 578a

-4	8	-3	5	-7	-11	13	17
4624f	18496g	5202a	14450g	28322ba	69938e	97682e	34a

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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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