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	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-150528 = -1 · 210 · 3 · 72	Discriminant
Eigenvalues	2- 3+ -4 7-  2  6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,21]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	-16384/147	j-invariant
L	2.0131740792278	L(r)(E,1)/r!
Ω	2.7800562144646	Real period
R	0.72414869481894	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	1344i1 336f1 4032bn1 33600gc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344o1

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 1344o1

-4	8	-3	5	-7
1344i1	336f1	4032bn1	33600gc1	9408dd1

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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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