Cremona's table of elliptic curves

28768 = 2⁵ · 29 · 31

Field	Data	Notes
Atkin-Lehner	2- 29- 31+	Signs for the Atkin-Lehner involutions
Class	28768h	Isogeny class
Conductor	28768	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	218624	Modular degree for the optimal curve
Δ	3268058354561024 = 212 · 29 · 317	Discriminant
Eigenvalues	2-  2  1 -2 -4  2 -1  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-166545,26071073]	[a1,a2,a3,a4,a6]
Generators	[329:2604:1]	Generators of the group modulo torsion
j	124727198695771456/797865809219	j-invariant
L	7.7900296660961	L(r)(E,1)/r!
Ω	0.44983228407381	Real period
R	4.3294078381543	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	28768e1 57536d1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 28768h1

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	-2	-4	2	-1	7	9	-	+	-9	6	-6	-13	14	0	-13	10	2	-1	-8	-1	7	-14

---

Quadratic twists for elliptic curve 28768h1

-4	8
28768e1	57536d1

---

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