Cremona's table of elliptic curves

1089 = 3² · 11²

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Class	1089a	Isogeny class
Conductor	1089	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-288178803 = -1 · 39 · 114	Discriminant
Eigenvalues	0 3+  0  5 11-  2  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,-817]	[a1,a2,a3,a4,a6]
j	0	j-invariant
L	1.5887181344624	L(r)(E,1)/r!
Ω	0.79435906723122	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	17424bg2 69696p2 1089a1 27225d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089a2

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
0	+	0	5	-	2	0	-7	0	0	11	11	0	8	0	0	0	-1	11	0	17	-13	0	0	5

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Quadratic twists for elliptic curve 1089a2

-4	8	-3	5	-7	-11
17424bg2	69696p2	1089a1	27225d2	53361g2	1089b2

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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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