Cremona's table of elliptic curves

1958 = 2 · 11 · 89

Field	Data	Notes
Atkin-Lehner	2- 11+ 89-	Signs for the Atkin-Lehner involutions
Class	1958a	Isogeny class
Conductor	1958	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	172304 = 24 · 112 · 89	Discriminant
Eigenvalues	2-  0 -2  0 11+  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-226,1361]	[a1,a2,a3,a4,a6]
Generators	[-9:55:1]	Generators of the group modulo torsion
j	1271294679537/172304	j-invariant
L	3.8233338140411	L(r)(E,1)/r!
Ω	3.1001766494773	Real period
R	2.4665264249931	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15664f1 62656f1 17622e1 48950d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1958a1

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	-2	0	+	2	2	0	0	-6	-8	2	-6	-8	0	6	-8	-14	-4	-8	-6	8	16	-	2

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Quadratic twists for elliptic curve 1958a1

-4	8	-3	5	-7	-11
15664f1	62656f1	17622e1	48950d1	95942w1	21538b1

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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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