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	60	Product of Tamagawa factors cp
deg	28800	Modular degree for the optimal curve
Δ	-3611226931200000 = -1 · 220 · 33 · 55 · 74 · 17	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,13157,-2831194]	[a1,a2,a3,a4,a6]
Generators	[160:1757:1]	Generators of the group modulo torsion
j	251907898698209879/3611226931200000	j-invariant
L	3.1924789504951	L(r)(E,1)/r!
Ω	0.21715904656121	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	28560cz1 114240h1 10710ba1 17850bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570m1

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 3570m1

-4	8	-3	5	-7	17
28560cz1	114240h1	10710ba1	17850bl1	24990h1	60690j1

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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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