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	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-28672 = -1 · 212 · 7	Discriminant
Eigenvalues	2- -2  0 7- -4  4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7,7]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	8000/7	j-invariant
L	1.4865234745167	L(r)(E,1)/r!
Ω	2.4289383121372	Real period
R	0.61200544579032	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	448d1 224b1 4032bg1 11200cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448g1

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 448g1

-4	8	-3	5	-7	-11	13	17
448d1	224b1	4032bg1	11200cb1	3136z1	54208ch1	75712cd1	129472cc1

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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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