Cremona's table of elliptic curves

867 = 3 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 17+	Signs for the Atkin-Lehner involutions
Class	867c	Isogeny class
Conductor	867	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-28816853988771 = -1 · 35 · 179	Discriminant
Eigenvalues	2 3+ -3  2 -5 -1 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-244012,-46313805]	[a1,a2,a3,a4,a6]
Generators	[154840973142:2440282876849:222545016]	Generators of the group modulo torsion
j	-13549359104/243	j-invariant
L	3.3192111932788	L(r)(E,1)/r!
Ω	0.10740293444166	Real period
R	15.452143884773	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	13872bm2 55488bo2 2601k2 21675r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 867c2

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
2	+	-3	2	-5	-1	+	-5	-1	-6	10	-2	-5	1	-2	6	0	10	-12	0	6	-4	6	-10	8

---

Quadratic twists for elliptic curve 867c2

-4	8	-3	5	-7	-11	17
13872bm2	55488bo2	2601k2	21675r2	42483y2	104907s2	867e2

---

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