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	13860b	Isogeny class
Conductor	13860	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	18074574524160 = 28 · 39 · 5 · 72 · 114	Discriminant
Eigenvalues	2- 3+ 5+ 7- 11+ -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8343,210222]	[a1,a2,a3,a4,a6]
Generators	[19:242:1]	Generators of the group modulo torsion
j	12745567728/3587045	j-invariant
L	4.2576778576882	L(r)(E,1)/r!
Ω	0.64258178980552	Real period
R	1.1043154156238	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	55440by2 13860h2 69300b2 97020s2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13860b2

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	-6	-6	4	6	2	6	4	8	-6	12	14	4	0	-12	4	0	2	4

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Quadratic twists for elliptic curve 13860b2

-4	-3	5	-7
55440by2	13860h2	69300b2	97020s2

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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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