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	1344k	Isogeny class
Conductor	1344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1806336 = 212 · 32 · 72	Discriminant
Eigenvalues	2- 3+  2 7+  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-57,-135]	[a1,a2,a3,a4,a6]
j	5088448/441	j-invariant
L	1.744581748021	L(r)(E,1)/r!
Ω	1.744581748021	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1344s2 672f1 4032be2 33600gv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1344k2

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

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Quadratic twists for elliptic curve 1344k2

-4	8	-3	5	-7
1344s2	672f1	4032be2	33600gv2	9408da2

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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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