Cremona's table of elliptic curves

448 = 2⁶ · 7

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	448g	Isogeny class
Conductor	448	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1605632 = 215 · 72	Discriminant
Eigenvalues	2- -2  0 7- -4  4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,31]	[a1,a2,a3,a4,a6]
Generators	[-1:8:1]	Generators of the group modulo torsion
j	125000/49	j-invariant
L	1.4865234745167	L(r)(E,1)/r!
Ω	2.4289383121372	Real period
R	0.30600272289516	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	448d2 224b2 4032bg2 11200cb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448g2

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	0	-	-4	4	-2	-6	-8	-2	4	-10	-10	4	-4	2	10	8	-8	0	-6	16	2	18	-2

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Quadratic twists for elliptic curve 448g2

-4	8	-3	5	-7	-11	13	17
448d2	224b2	4032bg2	11200cb2	3136z2	54208ch2	75712cd2	129472cc2

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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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