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
Δ	83607552 = 214 · 36 · 7	Discriminant
Eigenvalues	2+ 3+  0 7-  6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-113,-111]	[a1,a2,a3,a4,a6]
j	9826000/5103	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	1344p2 84a2 4032n2 33600cn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344d2

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 1344d2

-4	8	-3	5	-7
1344p2	84a2	4032n2	33600cn2	9408bb2

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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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