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	13860d	Isogeny class
Conductor	13860	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-146361600 = -1 · 28 · 33 · 52 · 7 · 112	Discriminant
Eigenvalues	2- 3+ 5+ 7- 11-  6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,57,558]	[a1,a2,a3,a4,a6]
j	2963088/21175	j-invariant
L	2.6674110267599	L(r)(E,1)/r!
Ω	1.3337055133799	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55440bx2 13860g2 69300h2 97020ba2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13860d2

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

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Quadratic twists for elliptic curve 13860d2

-4	-3	5	-7
55440bx2	13860g2	69300h2	97020ba2

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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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