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	1120	Product of Tamagawa factors cp
Δ	74880071980801920 = 27 · 35 · 5 · 78 · 174	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-843896,298027200]	[a1,a2,a3,a4,a6]
Generators	[-914:17950:1]	Generators of the group modulo torsion
j	66464620505913166201729/74880071980801920	j-invariant
L	5.5286220467775	L(r)(E,1)/r!
Ω	0.34336281036678	Real period
R	0.057505000956276	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	28560cl4 114240cn4 10710k3 17850a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570x4

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 3570x4

-4	8	-3	5	-7	17
28560cl4	114240cn4	10710k3	17850a4	24990bq4	60690bq4

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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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