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	2288g	Isogeny class
Conductor	2288	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-1171456 = -1 · 213 · 11 · 13	Discriminant
Eigenvalues	2- -2  1  3 11+ 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,0,52]	[a1,a2,a3,a4,a6]
Generators	[2:8:1]	Generators of the group modulo torsion
j	-1/286	j-invariant
L	2.5625470035398	L(r)(E,1)/r!
Ω	2.1821517835976	Real period
R	0.29358028882334	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	286f1 9152bb1 20592br1 57200bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288g1

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	1	3	+	-	-6	0	-1	-3	-10	2	7	1	4	6	5	-11	1	-16	-7	-4	-4	12	-16

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Quadratic twists for elliptic curve 2288g1

-4	8	-3	5	-7	-11	13
286f1	9152bb1	20592br1	57200bd1	112112bd1	25168bd1	29744be1

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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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