Cremona's table of elliptic curves

6489 = 3² · 7 · 103

Field	Data	Notes
Atkin-Lehner	3- 7- 103+	Signs for the Atkin-Lehner involutions
Class	6489d	Isogeny class
Conductor	6489	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3448520649 = 314 · 7 · 103	Discriminant
Eigenvalues	1 3- -2 7-  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-34623,-2471040]	[a1,a2,a3,a4,a6]
Generators	[3156010:37165505:10648]	Generators of the group modulo torsion
j	6296472729841393/4730481	j-invariant
L	4.2637551721458	L(r)(E,1)/r!
Ω	0.34999175407305	Real period
R	12.182444650556	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	103824bw4 2163b4 45423k4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6489d3

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
1	-	-2	-	0	-2	6	-4	8	2	-8	6	6	0	0	10	-12	6	-8	-12	-2	-16	-12	-6	-14

---

Quadratic twists for elliptic curve 6489d3

-4	-3	-7
103824bw4	2163b4	45423k4

---

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