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	3570j	Isogeny class
Conductor	3570	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3548222643000 = 23 · 3 · 53 · 72 · 176	Discriminant
Eigenvalues	2+ 3- 5+ 7- -6  2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15284,-722854]	[a1,a2,a3,a4,a6]
Generators	[1270:6771:8]	Generators of the group modulo torsion
j	394815279796185529/3548222643000	j-invariant
L	2.9320153026356	L(r)(E,1)/r!
Ω	0.4296147924361	Real period
R	6.8247540686618	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	28560ch4 114240ch4 10710bn4 17850bi4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570j4

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

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Quadratic twists for elliptic curve 3570j4

-4	8	-3	5	-7	17
28560ch4	114240ch4	10710bn4	17850bi4	24990q4	60690p4

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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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