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	570k	Isogeny class
Conductor	570	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-70568821500000000 = -1 · 28 · 3 · 59 · 196	Discriminant
Eigenvalues	2- 3- 5+  2  6 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,85489,8420985]	[a1,a2,a3,a4,a6]
j	69096190760262356111/70568821500000000	j-invariant
L	2.7435733370843	L(r)(E,1)/r!
Ω	0.22863111142369	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	4560n3 18240q3 1710j3 2850d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570k3

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

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Quadratic twists for elliptic curve 570k3

-4	8	-3	5	-7	-11	13	-19
4560n3	18240q3	1710j3	2850d3	27930cr3	68970x3	96330bn3	10830e3

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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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