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	144	Product of Tamagawa factors cp
Δ	886464000000 = 212 · 36 · 56 · 19	Discriminant
Eigenvalues	2- 3- 5+  2  6 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-414991,102863225]	[a1,a2,a3,a4,a6]
j	7903870428425797297009/886464000000	j-invariant
L	2.7435733370843	L(r)(E,1)/r!
Ω	0.68589333427107	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	4560n2 18240q2 1710j2 2850d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570k2

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 570k2

-4	8	-3	5	-7	-11	13	-19
4560n2	18240q2	1710j2	2850d2	27930cr2	68970x2	96330bn2	10830e2

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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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