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
deg	32	Modular degree for the optimal curve
Δ	-114688 = -1 · 214 · 7	Discriminant
Eigenvalues	2+  0 -2 7+  4 -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,4,16]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	432/7	j-invariant
L	1.7234498941954	L(r)(E,1)/r!
Ω	2.4735961737513	Real period
R	0.69673858347771	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	448b1 56a1 4032g1 11200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448a1

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 448a1

-4	8	-3	5	-7	-11	13	17
448b1	56a1	4032g1	11200n1	3136e1	54208be1	75712z1	129472z1

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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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