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	10080r	Isogeny class
Conductor	10080	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5740875000000000 = 29 · 38 · 512 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-52923,-2944622]	[a1,a2,a3,a4,a6]
Generators	[41558394378:-541475656250:119823157]	Generators of the group modulo torsion
j	43919722445768/15380859375	j-invariant
L	4.4434330187792	L(r)(E,1)/r!
Ω	0.32381627352599	Real period
R	13.722080642814	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	10080bn2 20160co4 3360z2 50400de3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080r3

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

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Quadratic twists for elliptic curve 10080r3

-4	8	-3	5	-7
10080bn2	20160co4	3360z2	50400de3	70560br3

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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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