Cremona's table of elliptic curves

3570 = 2 · 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7- 17-	Signs for the Atkin-Lehner involutions
Class	3570p	Isogeny class
Conductor	3570	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	118657634071410000 = 24 · 35 · 54 · 7 · 178	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-188653,-26848744]	[a1,a2,a3,a4,a6]
Generators	[-305:1682:1]	Generators of the group modulo torsion
j	742525803457216841161/118657634071410000	j-invariant
L	3.3064654916508	L(r)(E,1)/r!
Ω	0.23155156388093	Real period
R	0.17849509609397	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28560cu4 114240bc4 10710bb3 17850bc3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570p3

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

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Quadratic twists for elliptic curve 3570p3

-4	8	-3	5	-7	17
28560cu4	114240bc4	10710bb3	17850bc3	24990a4	60690c4

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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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