Cremona's table of elliptic curves

4872 = 2³ · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	4872a	Isogeny class
Conductor	4872	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-488291328 = -1 · 210 · 34 · 7 · 292	Discriminant
Eigenvalues	2+ 3+  0 7+  4  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,112,924]	[a1,a2,a3,a4,a6]
Generators	[26:144:1]	Generators of the group modulo torsion
j	150381500/476847	j-invariant
L	3.2585510762341	L(r)(E,1)/r!
Ω	1.1709744590122	Real period
R	1.3913843513645	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	9744d1 38976q1 14616i1 121800bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4872a1

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
+	+	0	+	4	0	0	0	0	+	-10	-10	4	-4	6	-10	6	10	16	8	12	4	-14	4	-8

---

Quadratic twists for elliptic curve 4872a1

-4	8	-3	5	-7
9744d1	38976q1	14616i1	121800bn1	34104n1

---

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