Cremona's table of elliptic curves

969 = 3 · 17 · 19

Field	Data	Notes
Atkin-Lehner	3- 17+ 19+	Signs for the Atkin-Lehner involutions
Class	969a	Isogeny class
Conductor	969	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	444771 = 34 · 172 · 19	Discriminant
Eigenvalues	1 3-  2  2  2  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-105,-419]	[a1,a2,a3,a4,a6]
j	126279339913/444771	j-invariant
L	2.9869009291835	L(r)(E,1)/r!
Ω	1.4934504645917	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15504n2 62016j2 2907a2 24225d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 969a2

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
1	-	2	2	2	2	+	+	6	0	-8	12	-4	12	-8	6	-4	-6	12	-8	-10	-12	-4	-6	8

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Quadratic twists for elliptic curve 969a2

-4	8	-3	5	-7	-11	17	-19
15504n2	62016j2	2907a2	24225d2	47481j2	117249bb2	16473b2	18411e2

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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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