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
deg	96	Modular degree for the optimal curve
Δ	397953 = 34 · 173	Discriminant
Eigenvalues	-1 3+  0 -4  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-23,20]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	274625/81	j-invariant
L	1.2964049615091	L(r)(E,1)/r!
Ω	2.7849176519372	Real period
R	0.46550926222445	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	13872bf1 55488be1 2601i1 21675q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 867b1

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 867b1

-4	8	-3	5	-7	-11	17
13872bf1	55488be1	2601i1	21675q1	42483t1	104907k1	867d1

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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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