Cremona's table of elliptic curves

13888 = 2⁶ · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	13888q	Isogeny class
Conductor	13888	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	19355546943488 = 223 · 74 · 312	Discriminant
Eigenvalues	2- -2  2 7+ -2  4 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8897,-246977]	[a1,a2,a3,a4,a6]
Generators	[527:11904:1]	Generators of the group modulo torsion
j	297141543217/73835552	j-invariant
L	3.4012588835958	L(r)(E,1)/r!
Ω	0.50051559971538	Real period
R	1.6988775602249	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	13888i2 3472e2 124992ff2 97216bu2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13888q2

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

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Quadratic twists for elliptic curve 13888q2

-4	8	-3	-7
13888i2	3472e2	124992ff2	97216bu2

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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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