Cremona's table of elliptic curves

2288 = 2⁴ · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	2288h	Isogeny class
Conductor	2288	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-51544064 = -1 · 215 · 112 · 13	Discriminant
Eigenvalues	2-  1 -1 -1 11- 13+ -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-536,-4972]	[a1,a2,a3,a4,a6]
Generators	[38:176:1]	Generators of the group modulo torsion
j	-4165509529/12584	j-invariant
L	3.3350275273891	L(r)(E,1)/r!
Ω	0.4959436015831	Real period
R	0.8405763066464	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	286c1 9152u1 20592z1 57200bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288h1

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
-	1	-1	-1	-	+	-1	4	8	-8	0	7	-8	-11	1	2	-14	-8	-8	-9	-4	-2	0	-4	8

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Quadratic twists for elliptic curve 2288h1

-4	8	-3	5	-7	-11	13
286c1	9152u1	20592z1	57200bw1	112112bs1	25168bg1	29744l1

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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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