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	1344d	Isogeny class
Conductor	1344	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-1354752 = -1 · 210 · 33 · 72	Discriminant
Eigenvalues	2+ 3+  0 7-  6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,-27]	[a1,a2,a3,a4,a6]
j	2048000/1323	j-invariant
L	1.5487880808399	L(r)(E,1)/r!
Ω	1.5487880808399	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1344p1 84a1 4032n1 33600cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344d1

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

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Quadratic twists for elliptic curve 1344d1

-4	8	-3	5	-7
1344p1	84a1	4032n1	33600cn1	9408bb1

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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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