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	10080t	Isogeny class
Conductor	10080	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3571283520000 = 29 · 313 · 54 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-918540003,-10715075262502]	[a1,a2,a3,a4,a6]
Generators	[-2709448393398245503535890012164551632987267617192540494:-2830333034362197885691357460432854152558597780783:154843319340215733625255738598528392265752489648072]	Generators of the group modulo torsion
j	229625675762164624948320008/9568125	j-invariant
L	4.2256714431698	L(r)(E,1)/r!
Ω	0.027423636010752	Real period
R	77.044332150429	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	10080n3 20160fi3 3360q3 50400df4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080t2

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	-6	-6	-4	4	2	8	6	-6	8	0	-6	4	10	8	-12	-14	-16	12	-14	18

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Quadratic twists for elliptic curve 10080t2

-4	8	-3	5	-7
10080n3	20160fi3	3360q3	50400df4	70560bs4

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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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