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	108	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	1214514000 = 24 · 36 · 53 · 72 · 17	Discriminant
Eigenvalues	2- 3- 5- 7-  0 -4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-645,5868]	[a1,a2,a3,a4,a6]
Generators	[-24:90:1]	Generators of the group modulo torsion
j	1857616347136/75907125	j-invariant
L	5.3004762200739	L(r)(E,1)/r!
Ω	1.5225516637442	Real period
R	1.1604370799125	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	28560cq1 114240u1 21420q1 35700g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140o1

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 7140o1

-4	8	-3	5	-7	17
28560cq1	114240u1	21420q1	35700g1	49980f1	121380a1

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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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