Cremona's table of elliptic curves

448 = 2⁶ · 7

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	448b	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	[4:8:1]	Generators of the group modulo torsion
j	432/7	j-invariant
L	1.7358759869411	L(r)(E,1)/r!
Ω	1.623666692621	Real period
R	1.0691085767972	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	448a1 112b1 4032bj1 11200bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448b1

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 448b1

-4	8	-3	5	-7	-11	13	17
448a1	112b1	4032bj1	11200bv1	3136s1	54208bx1	75712bs1	129472bv1

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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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