Cremona's table of elliptic curves

13858 = 2 · 13² · 41

Field	Data	Notes
Atkin-Lehner	2- 13+ 41-	Signs for the Atkin-Lehner involutions
Class	13858m	Isogeny class
Conductor	13858	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	791596676 = 22 · 136 · 41	Discriminant
Eigenvalues	2- -2  2  4  2 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-257,805]	[a1,a2,a3,a4,a6]
Generators	[-130:285:8]	Generators of the group modulo torsion
j	389017/164	j-invariant
L	6.6289736819211	L(r)(E,1)/r!
Ω	1.4391682835529	Real period
R	4.6061143492934	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	110864p1 124722n1 82a1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 13858m1

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	4	2	+	-2	-6	-8	0	8	-2	-	-12	-4	-4	-8	-14	2	-8	-10	4	-12	14	-6

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Quadratic twists for elliptic curve 13858m1

-4	-3	13
110864p1	124722n1	82a1

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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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