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	3570u	Isogeny class
Conductor	3570	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	2924544000 = 216 · 3 · 53 · 7 · 17	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1015,-12595]	[a1,a2,a3,a4,a6]
Generators	[-17:18:1]	Generators of the group modulo torsion
j	115650783909361/2924544000	j-invariant
L	4.5784494859945	L(r)(E,1)/r!
Ω	0.84713097825704	Real period
R	0.45038779947726	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	28560dv1 114240dy1 10710h1 17850p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570u1

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	-	0	4	-6	0	-6	-6	-4	-12	6	-4	-2	-4	0	2	4	0	-10	2

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Quadratic twists for elliptic curve 3570u1

-4	8	-3	5	-7	17
28560dv1	114240dy1	10710h1	17850p1	24990bz1	60690bt1

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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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