Cremona's table of elliptic curves

3003 = 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	3+ 7- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	3003f	Isogeny class
Conductor	3003	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	6552	Modular degree for the optimal curve
Δ	-899079608427 = -1 · 3 · 7 · 117 · 133	Discriminant
Eigenvalues	-2 3+  0 7- 11+ 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,1882,-33706]	[a1,a2,a3,a4,a6]
j	736803680768000/899079608427	j-invariant
L	0.47502370295132	L(r)(E,1)/r!
Ω	0.47502370295132	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48048ci1 9009m1 75075bh1 21021l1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3003f1

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	+	0	-	+	+	-6	-2	-4	7	5	10	-5	6	12	-14	-12	-11	4	-7	10	10	-7	-6	5

---

Quadratic twists for elliptic curve 3003f1

-4	-3	5	-7	-11	13
48048ci1	9009m1	75075bh1	21021l1	33033j1	39039k1

---

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