Cremona's table of elliptic curves

267 = 3 · 89

Field	Data	Notes
Atkin-Lehner	3+ 89-	Signs for the Atkin-Lehner involutions
Class	267b	Isogeny class
Conductor	267	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	238	Modular degree for the optimal curve
Δ	-11493474507 = -1 · 317 · 89	Discriminant
Eigenvalues	0 3+  4 -2  2  6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-441,6419]	[a1,a2,a3,a4,a6]
j	-9506571157504/11493474507	j-invariant
L	1.1529749720365	L(r)(E,1)/r!
Ω	1.1529749720365	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	4272e1 17088f1 801a1 6675g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 267b1

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	+	4	-2	2	6	4	-4	-3	3	8	-8	-11	8	-2	-8	-9	-12	3	10	1	-1	9	-	7

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Quadratic twists for elliptic curve 267b1

-4	8	-3	5	-7	-11	13	17	-19	89
4272e1	17088f1	801a1	6675g1	13083f1	32307d1	45123a1	77163c1	96387i1	23763c1

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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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