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	12	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	26261675072 = 26 · 177	Discriminant
Eigenvalues	2-  2  0  4 -6  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-873,5783]	[a1,a2,a3,a4,a6]
j	3048625/1088	j-invariant
L	3.2710755444012	L(r)(E,1)/r!
Ω	1.0903585148004	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4624f1 18496g1 5202a1 14450g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 578a1

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 578a1

-4	8	-3	5	-7	-11	13	17
4624f1	18496g1	5202a1	14450g1	28322ba1	69938e1	97682e1	34a1

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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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