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	1344o	Isogeny class
Conductor	1344	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1032192 = 214 · 32 · 7	Discriminant
Eigenvalues	2- 3+ -4 7-  2  6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-145,721]	[a1,a2,a3,a4,a6]
Generators	[1:24:1]	Generators of the group modulo torsion
j	20720464/63	j-invariant
L	2.0131740792278	L(r)(E,1)/r!
Ω	2.7800562144646	Real period
R	0.36207434740947	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1344i2 336f2 4032bn2 33600gc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344o2

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
-	+	-4	-	2	6	-4	-4	-2	2	0	-2	0	-4	-12	6	-8	-6	-8	-14	-2	-12	-4	0	-2

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Quadratic twists for elliptic curve 1344o2

-4	8	-3	5	-7
1344i2	336f2	4032bn2	33600gc2	9408dd2

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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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