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	16	Product of Tamagawa factors cp
Δ	8122500 = 22 · 32 · 54 · 192	Discriminant
Eigenvalues	2- 3+ 5+  0  4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-51,-51]	[a1,a2,a3,a4,a6]
j	14688124849/8122500	j-invariant
L	1.9129202434808	L(r)(E,1)/r!
Ω	1.9129202434808	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	4560x2 18240bn2 1710h2 2850i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570g2

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 570g2

-4	8	-3	5	-7	-11	13	-19
4560x2	18240bn2	1710h2	2850i2	27930dn2	68970e2	96330u2	10830l2

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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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