Cremona's table of elliptic curves

4761 = 3² · 23²

Field	Data	Notes
Atkin-Lehner	3+ 23-	Signs for the Atkin-Lehner involutions
Class	4761b	Isogeny class
Conductor	4761	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-14283 = -1 · 33 · 232	Discriminant
Eigenvalues	0 3+  0 -5  0 -7  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,-6]	[a1,a2,a3,a4,a6]
Generators	[2:1:1] [6:14:1]	Generators of the group modulo torsion
j	0	j-invariant
L	3.791654833547	L(r)(E,1)/r!
Ω	1.8144864954189	Real period
R	1.0448286176615	Regulator
r	2	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	76176bh1 4761b2 119025c1 4761a1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4761b1

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	+	0	-5	0	-7	0	-8	-	0	-4	-11	0	-5	0	0	0	1	-11	0	-10	4	0	0	-14

---

Quadratic twists for elliptic curve 4761b1

-4	-3	5	-23
76176bh1	4761b2	119025c1	4761a1

---

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