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
Δ	15183622322 = 2 · 112 · 894	Discriminant
Eigenvalues	2-  0 -2  0 11+  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1456,-20175]	[a1,a2,a3,a4,a6]
Generators	[510:2767:8]	Generators of the group modulo torsion
j	341136485041617/15183622322	j-invariant
L	3.8233338140411	L(r)(E,1)/r!
Ω	0.77504416236933	Real period
R	2.4665264249931	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15664f3 62656f4 17622e3 48950d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1958a3

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 1958a3

-4	8	-3	5	-7	-11
15664f3	62656f4	17622e3	48950d4	95942w4	21538b4

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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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