Cremona's table of elliptic curves

869 = 11 · 79

Field	Data	Notes
Atkin-Lehner	11+ 79+	Signs for the Atkin-Lehner involutions
Class	869b	Isogeny class
Conductor	869	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-68651 = -1 · 11 · 792	Discriminant
Eigenvalues	-2  1  1 -2 11+  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,10,-2]	[a1,a2,a3,a4,a6]
Generators	[11:39:1]	Generators of the group modulo torsion
j	99897344/68651	j-invariant
L	1.4849690043256	L(r)(E,1)/r!
Ω	1.9650475386437	Real period
R	0.37784556737761	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	13904j1 55616j1 7821d1 21725b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 869b1

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	1	1	-2	+	2	0	2	-9	0	-5	5	12	-8	4	-2	-13	-10	9	-1	-14	+	12	-9	-7

---

Quadratic twists for elliptic curve 869b1

-4	8	-3	5	-7	-11	-79
13904j1	55616j1	7821d1	21725b1	42581g1	9559e1	68651b1

---

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