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	3570r	Isogeny class
Conductor	3570	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	191329687500 = 22 · 3 · 58 · 74 · 17	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1726,-18577]	[a1,a2,a3,a4,a6]
Generators	[-23:109:1]	Generators of the group modulo torsion
j	568671957006049/191329687500	j-invariant
L	4.2664140456727	L(r)(E,1)/r!
Ω	0.76080186443154	Real period
R	1.4019465005059	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	28560dd3 114240en3 10710m4 17850q3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570r3

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

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Quadratic twists for elliptic curve 3570r3

-4	8	-3	5	-7	17
28560dd3	114240en3	10710m4	17850q3	24990cf3	60690ca3

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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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