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
deg	1632	Modular degree for the optimal curve
Δ	-355763629491 = -1 · 3 · 179	Discriminant
Eigenvalues	2 3+ -3  2 -5 -1 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,1638,-13693]	[a1,a2,a3,a4,a6]
Generators	[1806:4805:216]	Generators of the group modulo torsion
j	4096/3	j-invariant
L	3.3192111932788	L(r)(E,1)/r!
Ω	0.53701467220831	Real period
R	3.0904287769546	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	13872bm1 55488bo1 2601k1 21675r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 867c1

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 867c1

-4	8	-3	5	-7	-11	17
13872bm1	55488bo1	2601k1	21675r1	42483y1	104907s1	867e1

---

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