Cremona's table of elliptic curves

1449 = 3² · 7 · 23

Field	Data	Notes
Atkin-Lehner	3+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	1449b	Isogeny class
Conductor	1449	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	784	Modular degree for the optimal curve
Δ	-511420203 = -1 · 33 · 77 · 23	Discriminant
Eigenvalues	-2 3+ -2 7- -1  0 -4  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-381,3062]	[a1,a2,a3,a4,a6]
Generators	[-15:73:1]	Generators of the group modulo torsion
j	-226534772736/18941489	j-invariant
L	1.3395152445583	L(r)(E,1)/r!
Ω	1.6172479002884	Real period
R	0.059162024763506	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	23184u1 92736u1 1449a1 36225a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1449b1

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	+	-2	-	-1	0	-4	7	-	-4	-4	4	9	6	3	-11	-3	-13	6	4	-8	-16	-2	12	-10

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Quadratic twists for elliptic curve 1449b1

-4	8	-3	5	-7	-23
23184u1	92736u1	1449a1	36225a1	10143e1	33327d1

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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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