Cremona's table of elliptic curves

13860 = 2² · 3² · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 11+	Signs for the Atkin-Lehner involutions
Class	13860f	Isogeny class
Conductor	13860	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	10368	Modular degree for the optimal curve
Δ	69883506000 = 24 · 33 · 53 · 76 · 11	Discriminant
Eigenvalues	2- 3+ 5- 7- 11+  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1032,-1031]	[a1,a2,a3,a4,a6]
j	281370820608/161767375	j-invariant
L	2.7473171488075	L(r)(E,1)/r!
Ω	0.91577238293583	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	55440cg1 13860c3 69300a1 97020f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13860f1

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
-	+	-	-	+	2	6	-4	0	6	8	-10	-6	8	0	6	-6	-4	14	0	2	-10	6	18	8

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Quadratic twists for elliptic curve 13860f1

-4	-3	5	-7
55440cg1	13860c3	69300a1	97020f1

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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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