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	6489g	Isogeny class
Conductor	6489	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1408	Modular degree for the optimal curve
Δ	4730481 = 38 · 7 · 103	Discriminant
Eigenvalues	1 3-  2 7- -6  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-126,567]	[a1,a2,a3,a4,a6]
j	304821217/6489	j-invariant
L	2.4382902206967	L(r)(E,1)/r!
Ω	2.4382902206967	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	103824bn1 2163e1 45423h1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6489g1

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	-	-6	2	4	-4	0	-6	8	-2	4	12	0	8	6	-10	4	6	6	16	-18	2	-2

---

Quadratic twists for elliptic curve 6489g1

-4	-3	-7
103824bn1	2163e1	45423h1

---

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