Cremona's table of elliptic curves

867 = 3 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 17+	Signs for the Atkin-Lehner involutions
Class	867b	Isogeny class
Conductor	867	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-32234193 = -1 · 38 · 173	Discriminant
Eigenvalues	-1 3+  0 -4  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,62,224]	[a1,a2,a3,a4,a6]
Generators	[1:16:1]	Generators of the group modulo torsion
j	5359375/6561	j-invariant
L	1.2964049615091	L(r)(E,1)/r!
Ω	1.3924588259686	Real period
R	0.93101852444891	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	13872bf2 55488be2 2601i2 21675q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 867b2

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 867b2

-4	8	-3	5	-7	-11	17
13872bf2	55488be2	2601i2	21675q2	42483t2	104907k2	867d2

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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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