Cremona's table of elliptic curves

867 = 3 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 17+	Signs for the Atkin-Lehner involutions
Class	867a	Isogeny class
Conductor	867	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-355763629491 = -1 · 3 · 179	Discriminant
Eigenvalues	0 3+ -3  4  3 -1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-17147,-859018]	[a1,a2,a3,a4,a6]
Generators	[1578:14735:8]	Generators of the group modulo torsion
j	-23100424192/14739	j-invariant
L	1.6987250822621	L(r)(E,1)/r!
Ω	0.20859495104453	Real period
R	2.0359134698081	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13872bn2 55488bp2 2601g2 21675p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 867a2

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
0	+	-3	4	3	-1	+	-1	-9	-6	-2	4	3	-7	-6	-6	6	-8	-4	-12	-2	10	-6	0	16

---

Quadratic twists for elliptic curve 867a2

-4	8	-3	5	-7	-11	17
13872bn2	55488bp2	2601g2	21675p2	42483q2	104907j2	51a2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations