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	3264i	Isogeny class
Conductor	3264	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1534132224 = 216 · 34 · 172	Discriminant
Eigenvalues	2+ 3+ -2 -4 -4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-289,289]	[a1,a2,a3,a4,a6]
Generators	[-15:32:1] [-8:45:1]	Generators of the group modulo torsion
j	40873252/23409	j-invariant
L	3.1605669580311	L(r)(E,1)/r!
Ω	1.2895517088331	Real period
R	2.4509036251759	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3264be2 408b2 9792j2 81600dg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3264i2

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	-4	-6	-	-4	-4	6	-4	-10	-6	-4	-8	-6	4	14	12	-12	10	-4	-4	-6	-6

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Quadratic twists for elliptic curve 3264i2

-4	8	-3	5	17
3264be2	408b2	9792j2	81600dg2	55488bk2

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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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