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	2288d	Isogeny class
Conductor	2288	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	352	Modular degree for the optimal curve
Δ	-292864 = -1 · 211 · 11 · 13	Discriminant
Eigenvalues	2+ -2  3 -1 11- 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-144,-716]	[a1,a2,a3,a4,a6]
j	-162365474/143	j-invariant
L	1.3773203279363	L(r)(E,1)/r!
Ω	0.68866016396817	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1144c1 9152x1 20592e1 57200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288d1

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	3	-1	-	+	2	-4	3	7	-2	-2	7	-1	8	-6	3	-1	7	0	1	-4	8	4	-8

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Quadratic twists for elliptic curve 2288d1

-4	8	-3	5	-7	-11	13
1144c1	9152x1	20592e1	57200n1	112112u1	25168k1	29744c1

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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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