Cremona's table of elliptic curves

13448 = 2³ · 41²

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	13448b	Isogeny class
Conductor	13448	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-8176563434619904 = -1 · 210 · 418	Discriminant
Eigenvalues	2+ -2  2  2 -2 -6  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,12888,4318240]	[a1,a2,a3,a4,a6]
Generators	[520795:33633448:125]	Generators of the group modulo torsion
j	48668/1681	j-invariant
L	3.7605971399885	L(r)(E,1)/r!
Ω	0.31293379307554	Real period
R	6.0086146386254	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	26896b2 107584b2 121032n2 328b2	Quadratic twists by: -4 8 -3 41

Hecke Eigenvalues for elliptic curve 13448b2

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

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Quadratic twists for elliptic curve 13448b2

-4	8	-3	41
26896b2	107584b2	121032n2	328b2

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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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