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	560	Product of Tamagawa factors cp
Δ	232359312482640000 = 27 · 320 · 54 · 72 · 17	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-599416,-177162304]	[a1,a2,a3,a4,a6]
Generators	[-460:1364:1]	Generators of the group modulo torsion
j	23818189767728437646209/232359312482640000	j-invariant
L	5.5286220467775	L(r)(E,1)/r!
Ω	0.17168140518339	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	28560cl3 114240cn3 10710k4 17850a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570x3

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 3570x3

-4	8	-3	5	-7	17
28560cl3	114240cn3	10710k4	17850a3	24990bq3	60690bq3

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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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