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	13888m	Isogeny class
Conductor	13888	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-29125246976 = -1 · 227 · 7 · 31	Discriminant
Eigenvalues	2-  1 -3 7+  0  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-257,-8449]	[a1,a2,a3,a4,a6]
j	-7189057/111104	j-invariant
L	1.0112579306188	L(r)(E,1)/r!
Ω	0.50562896530938	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13888k1 3472d1 124992ep1 97216ce1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13888m1

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
-	1	-3	+	0	4	-6	2	3	-3	+	-2	12	-10	-3	-6	0	-8	-13	12	11	1	-9	-9	8

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Quadratic twists for elliptic curve 13888m1

-4	8	-3	-7
13888k1	3472d1	124992ep1	97216ce1

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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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