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	10080s	Isogeny class
Conductor	10080	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	514382400 = 26 · 38 · 52 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-633,6032]	[a1,a2,a3,a4,a6]
Generators	[-11:108:1]	Generators of the group modulo torsion
j	601211584/11025	j-invariant
L	4.8146762422952	L(r)(E,1)/r!
Ω	1.6519200949222	Real period
R	1.457296953132	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	10080m1 20160fj2 3360p1 50400dg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080s1

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

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Quadratic twists for elliptic curve 10080s1

-4	8	-3	5	-7
10080m1	20160fj2	3360p1	50400dg1	70560bt1

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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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