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	3570p	Isogeny class
Conductor	3570	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	-193555307298039120 = -1 · 24 · 320 · 5 · 74 · 172	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,63027,20277208]	[a1,a2,a3,a4,a6]
Generators	[-88:3792:1]	Generators of the group modulo torsion
j	27689398696638536759/193555307298039120	j-invariant
L	3.3064654916508	L(r)(E,1)/r!
Ω	0.23155156388093	Real period
R	0.71398038437588	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28560cu3 114240bc3 10710bb4 17850bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570p4

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

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Quadratic twists for elliptic curve 3570p4

-4	8	-3	5	-7	17
28560cu3	114240bc3	10710bb4	17850bc4	24990a3	60690c3

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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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