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	13858j	Isogeny class
Conductor	13858	Conductor
∏ cp	168	Product of Tamagawa factors cp
deg	366912	Modular degree for the optimal curve
Δ	-221208132089544704 = -1 · 221 · 137 · 412	Discriminant
Eigenvalues	2- -3 -1 -3 -6 13+  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-91968,-25022877]	[a1,a2,a3,a4,a6]
Generators	[5821:-446367:1] [491:6683:1]	Generators of the group modulo torsion
j	-17822531769561/45829062656	j-invariant
L	5.513197116405	L(r)(E,1)/r!
Ω	0.12753249209332	Real period
R	0.25731991090081	Regulator
r	2	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	110864i1 124722r1 1066c1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 13858j1

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
-	-3	-1	-3	-6	+	3	-4	-6	4	0	3	+	5	-7	-12	-6	-10	-8	-5	-16	-10	-6	-14	18

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Quadratic twists for elliptic curve 13858j1

-4	-3	13
110864i1	124722r1	1066c1

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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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