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	570f	Isogeny class
Conductor	570	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-110808000 = -1 · 26 · 36 · 53 · 19	Discriminant
Eigenvalues	2+ 3- 5-  2  0  2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-23,506]	[a1,a2,a3,a4,a6]
j	-1263214441/110808000	j-invariant
L	1.543923095703	L(r)(E,1)/r!
Ω	1.543923095703	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	4560r1 18240c1 1710o1 2850r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570f1

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	0	2	0	-	0	-6	2	2	0	8	0	6	-6	2	-4	0	14	2	6	-12	-10

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Quadratic twists for elliptic curve 570f1

-4	8	-3	5	-7	-11	13	-19
4560r1	18240c1	1710o1	2850r1	27930b1	68970cu1	96330cx1	10830x1

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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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