Cremona's table of elliptic curves

3264 = 2⁶ · 3 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17-	Signs for the Atkin-Lehner involutions
Class	3264j	Isogeny class
Conductor	3264	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-67682304 = -1 · 214 · 35 · 17	Discriminant
Eigenvalues	2+ 3+  3 -4 -1  5 17-  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-69,477]	[a1,a2,a3,a4,a6]
j	-2249728/4131	j-invariant
L	1.7450335637976	L(r)(E,1)/r!
Ω	1.7450335637976	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3264bf1 408d1 9792n1 81600de1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3264j1

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
+	+	3	-4	-1	5	-	7	1	-2	-6	-8	7	1	-6	2	10	-8	12	12	-14	10	14	8	12

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Quadratic twists for elliptic curve 3264j1

-4	8	-3	5	17
3264bf1	408d1	9792n1	81600de1	55488br1

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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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