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	16	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-123120 = -1 · 24 · 34 · 5 · 19	Discriminant
Eigenvalues	2- 3- 5-  4 -4 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10,20]	[a1,a2,a3,a4,a6]
j	-111284641/123120	j-invariant
L	3.0009972890661	L(r)(E,1)/r!
Ω	3.0009972890661	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4560u1 18240k1 1710d1 2850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570m1

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 570m1

-4	8	-3	5	-7	-11	13	-19
4560u1	18240k1	1710d1	2850b1	27930ch1	68970bi1	96330bf1	10830h1

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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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