Cremona's table of elliptic curves

570 = 2 · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 19-	Signs for the Atkin-Lehner involutions
Class	570i	Isogeny class
Conductor	570	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	165622259047500 = 22 · 320 · 54 · 19	Discriminant
Eigenvalues	2- 3+ 5-  4  0 -6  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-31160,2011565]	[a1,a2,a3,a4,a6]
j	3345930611358906241/165622259047500	j-invariant
L	2.2660609606948	L(r)(E,1)/r!
Ω	0.5665152401737	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	4560bc4 18240bd3 1710g4 2850l3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570i3

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
-	+	-	4	0	-6	2	-	8	2	-8	10	6	-8	0	-2	-12	-2	-12	-8	2	-16	-4	6	-10

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Quadratic twists for elliptic curve 570i3

-4	8	-3	5	-7	-11	13	-19
4560bc4	18240bd3	1710g4	2850l3	27930cw3	68970o3	96330c3	10830p4

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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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