Cremona's table of elliptic curves

7140 = 2² · 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	7140j	Isogeny class
Conductor	7140	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	45563251781250000 = 24 · 36 · 59 · 76 · 17	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11064621,-14169870720]	[a1,a2,a3,a4,a6]
Generators	[36090:1332555:8]	Generators of the group modulo torsion
j	9362964919254624808075264/2847703236328125	j-invariant
L	4.7091392141574	L(r)(E,1)/r!
Ω	0.082778094255605	Real period
R	6.3209680673036	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	28560cj3 114240ck3 21420w3 35700a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140j3

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

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Quadratic twists for elliptic curve 7140j3

-4	8	-3	5	-7	17
28560cj3	114240ck3	21420w3	35700a3	49980j3	121380m3

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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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