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	474351505988 = 22 · 179	Discriminant
Eigenvalues	2-  2  0  4 -6  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-29773,-1989473]	[a1,a2,a3,a4,a6]
j	120920208625/19652	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	4624f3 18496g3 5202a3 14450g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 578a3

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 578a3

-4	8	-3	5	-7	-11	13	17
4624f3	18496g3	5202a3	14450g3	28322ba3	69938e3	97682e3	34a3

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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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