Cremona's table of elliptic curves

288 = 2⁵ · 3²

Field	Data	Notes
Atkin-Lehner	2+ 3+	Signs for the Atkin-Lehner involutions
Class	288a	Isogeny class
Conductor	288	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-1728 = -1 · 26 · 33	Discriminant
Eigenvalues	2+ 3+ -4  0  0 -6 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,3,0]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	1.4121235928356	L(r)(E,1)/r!
Ω	2.8175842073531	Real period
R	0.50118239204718	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	288a1 576f2 288e1 7200ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 288a1

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
+	+	-4	0	0	-6	-8	0	0	4	0	-2	8	0	0	4	0	-10	0	0	6	0	0	-16	-18

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Quadratic twists for elliptic curve 288a1

-4	8	-3	5	-7	-11	13	17	-19
288a1	576f2	288e1	7200ba1	14112i1	34848bo1	48672bh1	83232c1	103968bg1

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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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