Cremona's table of elliptic curves

448 = 2⁶ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	448a	Isogeny class
Conductor	448	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	917504 = 217 · 7	Discriminant
Eigenvalues	2+  0 -2 7+  4 -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1196,15920]	[a1,a2,a3,a4,a6]
Generators	[29:75:1]	Generators of the group modulo torsion
j	1443468546/7	j-invariant
L	1.7234498941954	L(r)(E,1)/r!
Ω	2.4735961737513	Real period
R	2.7869543339108	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	448b3 56a4 4032g3 11200n4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448a4

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	+	4	-2	-6	-8	0	-6	8	2	2	4	-8	-6	0	6	4	-8	10	16	-8	-6	-6

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Quadratic twists for elliptic curve 448a4

-4	8	-3	5	-7	-11	13	17
448b3	56a4	4032g3	11200n4	3136e3	54208be4	75712z4	129472z4

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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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