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	7140o	Isogeny class
Conductor	7140	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-158960374406400 = -1 · 28 · 3 · 52 · 73 · 176	Discriminant
Eigenvalues	2- 3- 5- 7-  0 -4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2700,-609900]	[a1,a2,a3,a4,a6]
Generators	[1642:21945:8]	Generators of the group modulo torsion
j	-8506205668816/620938962525	j-invariant
L	5.3004762200739	L(r)(E,1)/r!
Ω	0.25375861062404	Real period
R	6.9626224794752	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	28560cq4 114240u4 21420q4 35700g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140o4

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	-4	2	-6	-10	-6	-12	-12	-4	14	12	2	14	6	-6	2

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Quadratic twists for elliptic curve 7140o4

-4	8	-3	5	-7	17
28560cq4	114240u4	21420q4	35700g4	49980f4	121380a4

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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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