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	32	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	2893401000000 = 26 · 310 · 56 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-47253,-3952748]	[a1,a2,a3,a4,a6]
Generators	[14146:590121:8]	Generators of the group modulo torsion
j	250094631024064/62015625	j-invariant
L	4.4434330187792	L(r)(E,1)/r!
Ω	0.32381627352599	Real period
R	6.861040321407	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10080bn1 20160co2 3360z1 50400de1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080r1

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 10080r1

-4	8	-3	5	-7
10080bn1	20160co2	3360z1	50400de1	70560br1

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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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