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	96	Product of Tamagawa factors cp
Δ	-37652343750000 = -1 · 24 · 34 · 512 · 7 · 17	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,7225,179885]	[a1,a2,a3,a4,a6]
Generators	[33:658:1]	Generators of the group modulo torsion
j	41709358422320399/37652343750000	j-invariant
L	4.5784494859945	L(r)(E,1)/r!
Ω	0.42356548912852	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	28560dv3 114240dy3 10710h4 17850p4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570u4

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 3570u4

-4	8	-3	5	-7	17
28560dv3	114240dy3	10710h4	17850p4	24990bz3	60690bt3

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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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