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	2	Product of Tamagawa factors cp
Δ	917504 = 217 · 7	Discriminant
Eigenvalues	2-  0 -2 7- -4 -2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1196,-15920]	[a1,a2,a3,a4,a6]
Generators	[124:1320:1]	Generators of the group modulo torsion
j	1443468546/7	j-invariant
L	1.7358759869411	L(r)(E,1)/r!
Ω	0.81183334631051	Real period
R	4.2764343071889	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	448a4 112b3 4032bj4 11200bv3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 448b3

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 448b3

-4	8	-3	5	-7	-11	13	17
448a4	112b3	4032bj4	11200bv3	3136s4	54208bx4	75712bs4	129472bv4

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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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