Cremona's table of elliptic curves

578 = 2 · 17²

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	578a	Isogeny class
Conductor	578	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1165244474459522 = 2 · 1712	Discriminant
Eigenvalues	2-  2  0  4 -6  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-32663,-1583717]	[a1,a2,a3,a4,a6]
j	159661140625/48275138	j-invariant
L	3.2710755444012	L(r)(E,1)/r!
Ω	0.3634528382668	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4624f4 18496g4 5202a4 14450g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 578a4

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 elliptic curve 578a4

-4	8	-3	5	-7	-11	13	17
4624f4	18496g4	5202a4	14450g4	28322ba4	69938e4	97682e4	34a4

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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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