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	1344b	Isogeny class
Conductor	1344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	7225344 = 214 · 32 · 72	Discriminant
Eigenvalues	2+ 3+ -2 7+  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49,49]	[a1,a2,a3,a4,a6]
Generators	[-5:12:1]	Generators of the group modulo torsion
j	810448/441	j-invariant
L	2.1203229858127	L(r)(E,1)/r!
Ω	2.0523949268586	Real period
R	1.033096972744	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	1344t2 168a2 4032f2 33600cr2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344b2

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	+	0	2	6	4	-4	-6	-8	10	-10	-12	-8	-6	-4	10	-12	4	2	8	-4	6	10

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Quadratic twists for elliptic curve 1344b2

-4	8	-3	5	-7
1344t2	168a2	4032f2	33600cr2	9408bd2

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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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