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	12	Product of Tamagawa factors cp
Δ	-361417728 = -1 · 210 · 3 · 76	Discriminant
Eigenvalues	2+ 3+  0 7-  6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-453,-3675]	[a1,a2,a3,a4,a6]
j	-10061824000/352947	j-invariant
L	1.5487880808399	L(r)(E,1)/r!
Ω	0.5162626936133	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	1344p3 84a3 4032n3 33600cn3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344d3

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 1344d3

-4	8	-3	5	-7
1344p3	84a3	4032n3	33600cn3	9408bb3

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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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