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	10080cf	Isogeny class
Conductor	10080	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	104509440 = 212 · 36 · 5 · 7	Discriminant
Eigenvalues	2- 3- 5- 7- -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1692,-26784]	[a1,a2,a3,a4,a6]
Generators	[120:1224:1]	Generators of the group modulo torsion
j	179406144/35	j-invariant
L	4.7288581279494	L(r)(E,1)/r!
Ω	0.74439688852268	Real period
R	3.1763016482607	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	10080y3 20160br1 1120c3 50400bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080cf2

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	-6	-4	8	-6	0	10	-10	12	0	6	-12	2	4	12	-10	-4	0	-18	-10

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Quadratic twists for elliptic curve 10080cf2

-4	8	-3	5	-7
10080y3	20160br1	1120c3	50400bc4	70560dn4

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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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