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	10080bo	Isogeny class
Conductor	10080	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-307385777664000 = -1 · 212 · 36 · 53 · 77	Discriminant
Eigenvalues	2- 3- 5+ 7+ -5  5  5  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13368,1032208]	[a1,a2,a3,a4,a6]
Generators	[96:796:1]	Generators of the group modulo torsion
j	-88478050816/102942875	j-invariant
L	3.927693502702	L(r)(E,1)/r!
Ω	0.49366433993181	Real period
R	3.9781012977811	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	10080bs1 20160ey1 1120f1 50400bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080bo1

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
-	-	+	+	-5	5	5	0	-8	1	2	4	-2	4	-13	8	-4	-2	-8	12	-6	11	-8	18	-5

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Quadratic twists for elliptic curve 10080bo1

-4	8	-3	5	-7
10080bs1	20160ey1	1120f1	50400bt1	70560eg1

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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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