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	7140f	Isogeny class
Conductor	7140	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	149760	Modular degree for the optimal curve
Δ	233029039745250000 = 24 · 313 · 56 · 7 · 174	Discriminant
Eigenvalues	2- 3+ 5- 7-  2  0 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3708045,-2746975518]	[a1,a2,a3,a4,a6]
Generators	[19882:465205:8]	Generators of the group modulo torsion
j	352402381449896711028736/14564314984078125	j-invariant
L	3.9871363239569	L(r)(E,1)/r!
Ω	0.10879636186866	Real period
R	6.1079498362427	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	28560dq1 114240dq1 21420n1 35700z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140f1

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
-	+	-	-	2	0	-	-6	4	-6	-6	-6	6	-4	0	-12	8	-14	-4	-6	-4	16	-12	2	-16

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Quadratic twists for elliptic curve 7140f1

-4	8	-3	5	-7	17
28560dq1	114240dq1	21420n1	35700z1	49980s1	121380v1

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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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