Cremona's table of elliptic curves

6890 = 2 · 5 · 13 · 53

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+ 53+	Signs for the Atkin-Lehner involutions
Class	6890a	Isogeny class
Conductor	6890	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	1128857600 = 216 · 52 · 13 · 53	Discriminant
Eigenvalues	2+  2 5+  2 -2 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-273,533]	[a1,a2,a3,a4,a6]
Generators	[-7:50:1]	Generators of the group modulo torsion
j	2263054145689/1128857600	j-invariant
L	4.1433622086529	L(r)(E,1)/r!
Ω	1.3694309068216	Real period
R	3.0256088043678	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55120g1 62010cf1 34450v1 89570z1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890a1

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	+	2	-2	+	6	-8	2	-10	4	2	10	-8	6	+	-10	-14	8	-16	10	-2	4	-6	10

---

Quadratic twists for elliptic curve 6890a1

-4	-3	5	13
55120g1	62010cf1	34450v1	89570z1

---

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