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	10080cb	Isogeny class
Conductor	10080	Conductor
∏ cp	110	Product of Tamagawa factors cp
deg	147840	Modular degree for the optimal curve
Δ	-2450460600000000000 = -1 · 212 · 36 · 511 · 75	Discriminant
Eigenvalues	2- 3- 5- 7- -1 -1  3  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,269208,-52744176]	[a1,a2,a3,a4,a6]
Generators	[208:3500:1]	Generators of the group modulo torsion
j	722603599520256/820654296875	j-invariant
L	5.0309920861964	L(r)(E,1)/r!
Ω	0.13885798504788	Real period
R	0.3293745885548	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10080x1 20160bo1 1120e1 50400u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080cb1

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
-	-	-	-	-1	-1	3	8	-4	-3	-6	-8	-10	-12	-3	-12	0	2	4	12	-10	-13	0	6	5

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Quadratic twists for elliptic curve 10080cb1

-4	8	-3	5	-7
10080x1	20160bo1	1120e1	50400u1	70560cx1

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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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