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	7140c	Isogeny class
Conductor	7140	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	76438812240 = 24 · 34 · 5 · 74 · 173	Discriminant
Eigenvalues	2- 3+ 5+ 7+  2 -2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8041,-274550]	[a1,a2,a3,a4,a6]
Generators	[-51:17:1]	Generators of the group modulo torsion
j	3594081530527744/4777425765	j-invariant
L	3.1621596406887	L(r)(E,1)/r!
Ω	0.5041992608777	Real period
R	0.69684963555085	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	28560dn1 114240eh1 21420t1 35700bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7140c1

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	-2	-	0	4	-2	-2	-10	10	-10	-2	-2	-8	6	6	6	6	10	14	14	2

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Quadratic twists for elliptic curve 7140c1

-4	8	-3	5	-7	17
28560dn1	114240eh1	21420t1	35700bf1	49980bb1	121380bf1

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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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