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	570g	Isogeny class
Conductor	570	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	44531250 = 2 · 3 · 58 · 19	Discriminant
Eigenvalues	2- 3+ 5+  0  4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-621,-6207]	[a1,a2,a3,a4,a6]
j	26487576322129/44531250	j-invariant
L	1.9129202434808	L(r)(E,1)/r!
Ω	0.95646012174039	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4560x3 18240bn3 1710h3 2850i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570g3

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

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Quadratic twists for elliptic curve 570g3

-4	8	-3	5	-7	-11	13	-19
4560x3	18240bn3	1710h3	2850i3	27930dn4	68970e4	96330u4	10830l3

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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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