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	3570s	Isogeny class
Conductor	3570	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	537144431250000 = 24 · 3 · 58 · 73 · 174	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-91571,10568993]	[a1,a2,a3,a4,a6]
Generators	[257:1894:1]	Generators of the group modulo torsion
j	84917632843343402929/537144431250000	j-invariant
L	4.2528332597144	L(r)(E,1)/r!
Ω	0.52287987139262	Real period
R	0.67779004515694	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	28560df3 114240eo3 10710n3 17850r4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570s4

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

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Quadratic twists for elliptic curve 3570s4

-4	8	-3	5	-7	17
28560df3	114240eo3	10710n3	17850r4	24990cg3	60690cb3

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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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