Cremona's table of elliptic curves

10080 = 2⁵ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7-	Signs for the Atkin-Lehner involutions
Class	10080cf	Isogeny class
Conductor	10080	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1632960000 = 29 · 36 · 54 · 7	Discriminant
Eigenvalues	2- 3- 5- 7- -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-747,7614]	[a1,a2,a3,a4,a6]
Generators	[-27:90:1]	Generators of the group modulo torsion
j	123505992/4375	j-invariant
L	4.7288581279494	L(r)(E,1)/r!
Ω	1.4887937770454	Real period
R	0.79407541206517	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	10080y2 20160br3 1120c2 50400bc3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080cf3

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
-	-	-	-	-4	2	-6	-4	8	-6	0	10	-10	12	0	6	-12	2	4	12	-10	-4	0	-18	-10

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Quadratic twists for elliptic curve 10080cf3

-4	8	-3	5	-7
10080y2	20160br3	1120c2	50400bc3	70560dn3

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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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