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	570m	Isogeny class
Conductor	570	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	488703750 = 2 · 3 · 54 · 194	Discriminant
Eigenvalues	2- 3- 5-  4 -4 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-220,650]	[a1,a2,a3,a4,a6]
j	1177918188481/488703750	j-invariant
L	3.0009972890661	L(r)(E,1)/r!
Ω	1.500498644533	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	4560u4 18240k3 1710d4 2850b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570m3

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	-4	-2	-2	+	-8	6	4	-10	-2	12	0	6	0	-10	-4	-8	2	-12	-8	6	18

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Quadratic twists for elliptic curve 570m3

-4	8	-3	5	-7	-11	13	-19
4560u4	18240k3	1710d4	2850b3	27930ch3	68970bi3	96330bf3	10830h4

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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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