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	4	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	55233 = 32 · 17 · 192	Discriminant
Eigenvalues	1 3-  2  2  2  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-10,-1]	[a1,a2,a3,a4,a6]
j	95443993/55233	j-invariant
L	2.9869009291835	L(r)(E,1)/r!
Ω	2.9869009291835	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	15504n1 62016j1 2907a1 24225d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 969a1

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 969a1

-4	8	-3	5	-7	-11	17	-19
15504n1	62016j1	2907a1	24225d1	47481j1	117249bb1	16473b1	18411e1

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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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