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	1344a	Isogeny class
Conductor	1344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5664669696 = 218 · 32 · 74	Discriminant
Eigenvalues	2+ 3+  2 7+ -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3137,-66495]	[a1,a2,a3,a4,a6]
Generators	[67:140:1]	Generators of the group modulo torsion
j	13027640977/21609	j-invariant
L	2.4893223729121	L(r)(E,1)/r!
Ω	0.63797352449584	Real period
R	3.9019211257697	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1344r4 21a2 4032h4 33600dd4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344a3

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
+	+	2	+	-4	2	-6	-4	0	2	0	-6	2	4	0	-6	-12	2	-4	0	-6	-16	12	-14	18

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Quadratic twists for elliptic curve 1344a3

-4	8	-3	5	-7
1344r4	21a2	4032h4	33600dd4	9408bj4

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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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