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	10080bj	Isogeny class
Conductor	10080	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	5788125000000 = 26 · 33 · 510 · 73	Discriminant
Eigenvalues	2- 3+ 5- 7+  4  0 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4497,-8636]	[a1,a2,a3,a4,a6]
Generators	[-57:250:1]	Generators of the group modulo torsion
j	5820343774272/3349609375	j-invariant
L	4.8583106090467	L(r)(E,1)/r!
Ω	0.63433506166605	Real period
R	0.76589028458975	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	10080h1 20160f2 10080c1 50400i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080bj1

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	0	-2	2	-6	-4	-2	-10	10	4	-4	-2	-12	-10	-12	0	4	16	4	-6	-8

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Quadratic twists for elliptic curve 10080bj1

-4	8	-3	5	-7
10080h1	20160f2	10080c1	50400i1	70560ci1

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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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