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	3570x	Isogeny class
Conductor	3570	Conductor
∏ cp	280	Product of Tamagawa factors cp
deg	17920	Modular degree for the optimal curve
Δ	-271682182840320 = -1 · 228 · 35 · 5 · 72 · 17	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,15624,254016]	[a1,a2,a3,a4,a6]
Generators	[0:504:1]	Generators of the group modulo torsion
j	421792317902132351/271682182840320	j-invariant
L	5.5286220467775	L(r)(E,1)/r!
Ω	0.34336281036678	Real period
R	0.2300200038251	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	28560cl1 114240cn1 10710k1 17850a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570x1

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

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Quadratic twists for elliptic curve 3570x1

-4	8	-3	5	-7	17
28560cl1	114240cn1	10710k1	17850a1	24990bq1	60690bq1

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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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