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	3264b	Isogeny class
Conductor	3264	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	10027008 = 216 · 32 · 17	Discriminant
Eigenvalues	2+ 3+  0  2  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-193,-959]	[a1,a2,a3,a4,a6]
Generators	[-8:3:1]	Generators of the group modulo torsion
j	12194500/153	j-invariant
L	3.0865936240075	L(r)(E,1)/r!
Ω	1.2813047440605	Real period
R	1.2044728774772	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	3264w1 408a1 9792q1 81600dx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3264b1

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
+	+	0	2	0	-2	+	-4	2	0	6	0	-10	-4	-4	2	4	0	-4	-2	-14	6	12	-2	-2

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Quadratic twists for elliptic curve 3264b1

-4	8	-3	5	17
3264w1	408a1	9792q1	81600dx1	55488bd1

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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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