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	13858a	Isogeny class
Conductor	13858	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1291459454509366792 = -1 · 23 · 1314 · 41	Discriminant
Eigenvalues	2+  0  2  0  0 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,195079,-43518955]	[a1,a2,a3,a4,a6]
Generators	[3493193973247550:-196847298418509913:1141166125000]	Generators of the group modulo torsion
j	170095924504143/267559676488	j-invariant
L	3.8191825016478	L(r)(E,1)/r!
Ω	0.14351931246561	Real period
R	26.610930863838	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	110864e3 124722bu3 1066e4	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 13858a4

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
+	0	2	0	0	+	-6	8	0	10	0	-6	+	-4	8	-6	12	-10	-8	-8	-10	8	12	-2	-18

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Quadratic twists for elliptic curve 13858a4

-4	-3	13
110864e3	124722bu3	1066e4

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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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