Cremona's table of elliptic curves

288 = 2⁵ · 3²

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	288d	Isogeny class
Conductor	288	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-2985984 = -1 · 212 · 36	Discriminant
Eigenvalues	2+ 3-  2  0  0  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,36,0]	[a1,a2,a3,a4,a6]
j	1728	j-invariant
L	1.5138456348012	L(r)(E,1)/r!
Ω	1.5138456348012	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	288d4 576h1 32a1 7200bg4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 288d4

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	0	6	-2	0	0	10	0	-2	-10	0	0	-14	0	-10	0	0	-6	0	0	-10	18

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Quadratic twists for elliptic curve 288d4

-4	8	-3	5	-7	-11	13	17	-19
288d4	576h1	32a1	7200bg4	14112x4	34848ca2	48672bt2	83232n2	103968bz2

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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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