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	2288f	Isogeny class
Conductor	2288	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-57584384 = -1 · 28 · 113 · 132	Discriminant
Eigenvalues	2- -1  3 -2 11+ 13-  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,91,121]	[a1,a2,a3,a4,a6]
Generators	[5:26:1]	Generators of the group modulo torsion
j	321978368/224939	j-invariant
L	2.9307210990531	L(r)(E,1)/r!
Ω	1.2534289002054	Real period
R	0.58454075428067	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	572a1 9152z1 20592bx1 57200y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288f1

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	3	-2	+	-	0	-2	3	-6	1	-7	6	-8	-12	-6	-9	2	7	3	8	4	12	-15	-13

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Quadratic twists for elliptic curve 2288f1

-4	8	-3	5	-7	-11	13
572a1	9152z1	20592bx1	57200y1	112112bb1	25168ba1	29744bb1

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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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