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	3570m	Isogeny class
Conductor	3570	Conductor
∏ cp	120	Product of Tamagawa factors cp
Δ	31070538632700000 = 25 · 312 · 55 · 7 · 174	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3737723,-2781668122]	[a1,a2,a3,a4,a6]
Generators	[-1116:670:1]	Generators of the group modulo torsion
j	5774905528848578698851241/31070538632700000	j-invariant
L	3.1924789504951	L(r)(E,1)/r!
Ω	0.1085795232806	Real period
R	0.98007397528804	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	28560cz4 114240h4 10710ba4 17850bl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570m3

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

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Quadratic twists for elliptic curve 3570m3

-4	8	-3	5	-7	17
28560cz4	114240h4	10710ba4	17850bl3	24990h4	60690j4

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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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