Cremona's table of elliptic curves

10680 = 2³ · 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 89-	Signs for the Atkin-Lehner involutions
Class	10680a	Isogeny class
Conductor	10680	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	1167858000 = 24 · 38 · 53 · 89	Discriminant
Eigenvalues	2+ 3+ 5-  0 -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3735,89100]	[a1,a2,a3,a4,a6]
Generators	[-45:405:1]	Generators of the group modulo torsion
j	360239905232896/72991125	j-invariant
L	3.8059111657114	L(r)(E,1)/r!
Ω	1.4979446598595	Real period
R	0.8469185072272	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	21360e1 85440q1 32040g1 53400s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10680a1

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
+	+	-	0	-4	2	-6	-4	0	6	8	-6	10	12	-12	14	4	-2	-8	16	10	-8	-12	-	-6

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Quadratic twists for elliptic curve 10680a1

-4	8	-3	5
21360e1	85440q1	32040g1	53400s1

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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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