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	10080bn	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	[-1:2000:1]	Generators of the group modulo torsion
j	250094631024064/62015625	j-invariant
L	3.7971530989103	L(r)(E,1)/r!
Ω	0.78386578295062	Real period
R	2.4220684085847	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	10080r1 20160ca2 3360f1 50400br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080bn1

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 10080bn1

-4	8	-3	5	-7
10080r1	20160ca2	3360f1	50400br1	70560ee1

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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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