Cremona's table of elliptic curves

867 = 3 · 17²

Field	Data	Notes
Atkin-Lehner	3- 17+	Signs for the Atkin-Lehner involutions
Class	867d	Isogeny class
Conductor	867	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-778055057696817 = -1 · 38 · 179	Discriminant
Eigenvalues	-1 3-  0  4 -4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,17912,976001]	[a1,a2,a3,a4,a6]
j	5359375/6561	j-invariant
L	1.3508834867746	L(r)(E,1)/r!
Ω	0.33772087169365	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	13872r2 55488c2 2601h2 21675d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 867d2

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	-	0	4	-4	2	+	4	4	0	-4	8	8	4	-8	-6	12	8	12	12	0	4	-12	-10	16

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Quadratic twists for elliptic curve 867d2

-4	8	-3	5	-7	-11	17
13872r2	55488c2	2601h2	21675d2	42483l2	104907be2	867b2

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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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