Cremona's table of elliptic curves

1344 = 2⁶ · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	1344n	Isogeny class
Conductor	1344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	16257024 = 212 · 34 · 72	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-89,-231]	[a1,a2,a3,a4,a6]
Generators	[-5:8:1]	Generators of the group modulo torsion
j	19248832/3969	j-invariant
L	2.1824732328065	L(r)(E,1)/r!
Ω	1.5754380199059	Real period
R	1.385312024485	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1344q2 672h1 4032bi2 33600fx2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344n2

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	-2	2	4	0	-6	0	-6	-6	8	-8	-6	-12	-10	16	8	-6	-8	-12	-14	-6

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Quadratic twists for elliptic curve 1344n2

-4	8	-3	5	-7
1344q2	672h1	4032bi2	33600fx2	9408cu2

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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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