Cremona's table of elliptic curves

288 = 2⁵ · 3²

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	288c	Isogeny class
Conductor	288	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-30233088 = -1 · 29 · 310	Discriminant
Eigenvalues	2+ 3- -2  4  4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,69,146]	[a1,a2,a3,a4,a6]
j	97336/81	j-invariant
L	1.3526394018325	L(r)(E,1)/r!
Ω	1.3526394018325	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	288b4 576b4 96b4 7200bq4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 288c4

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	-2	6	4	0	-2	-4	-2	-2	-4	8	-10	-4	6	-4	-16	-6	-4	12	-10	-14

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Quadratic twists for elliptic curve 288c4

-4	8	-3	5	-7	-11	13	17	-19
288b4	576b4	96b4	7200bq4	14112v4	34848cg2	48672bs2	83232m2	103968cg2

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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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