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	8	Product of Tamagawa factors cp
Δ	3211264 = 216 · 72	Discriminant
Eigenvalues	2+  0 -2 7+  4 -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-76,240]	[a1,a2,a3,a4,a6]
Generators	[-3:21:1]	Generators of the group modulo torsion
j	740772/49	j-invariant
L	1.7234498941954	L(r)(E,1)/r!
Ω	2.4735961737513	Real period
R	1.3934771669554	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	448b2 56a2 4032g2 11200n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448a2

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 448a2

-4	8	-3	5	-7	-11	13	17
448b2	56a2	4032g2	11200n2	3136e2	54208be2	75712z2	129472z2

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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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