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	10080bm	Isogeny class
Conductor	10080	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	14696640000 = 29 · 38 · 54 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6123,-184322]	[a1,a2,a3,a4,a6]
Generators	[98:396:1]	Generators of the group modulo torsion
j	68017239368/39375	j-invariant
L	4.1725567794684	L(r)(E,1)/r!
Ω	0.53972629876813	Real period
R	3.8654377125886	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	10080u3 20160cc3 3360m3 50400bm4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080bm2

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

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Quadratic twists for elliptic curve 10080bm2

-4	8	-3	5	-7
10080u3	20160cc3	3360m3	50400bm4	70560ed4

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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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