Cremona's table of elliptic curves

288 = 2⁵ · 3²

Field	Data	Notes
Atkin-Lehner	2- 3-	Signs for the Atkin-Lehner involutions
Class	288b	Isogeny class
Conductor	288	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	8957952 = 212 · 37	Discriminant
Eigenvalues	2- 3- -2 -4 -4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156,736]	[a1,a2,a3,a4,a6]
Generators	[-10:36:1]	Generators of the group modulo torsion
j	140608/3	j-invariant
L	1.4337635566386	L(r)(E,1)/r!
Ω	2.3118891803439	Real period
R	0.62016967284967	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	288c2 576c1 96a2 7200o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 288b3

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 288b3

-4	8	-3	5	-7	-11	13	17	-19
288c2	576c1	96a2	7200o3	14112ca2	34848ba3	48672r3	83232bn3	103968z3

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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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