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	570l	Isogeny class
Conductor	570	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2228489100 = 22 · 32 · 52 · 195	Discriminant
Eigenvalues	2- 3- 5- -2  2  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-52823445,-147775056075]	[a1,a2,a3,a4,a6]
j	16300610738133468173382620881/2228489100	j-invariant
L	2.800031251919	L(r)(E,1)/r!
Ω	0.05600062503838	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	25	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4560s4 18240h4 1710c4 2850a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570l4

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	2	4	-2	+	4	0	-8	8	-8	-6	-12	-6	0	2	8	-8	14	0	4	0	-12

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Quadratic twists for elliptic curve 570l4

-4	8	-3	5	-7	-11	13	-19
4560s4	18240h4	1710c4	2850a4	27930cd4	68970bg4	96330bc4	10830g4

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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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