Cremona's table of elliptic curves

4720 = 2⁴ · 5 · 59

Field	Data	Notes
Atkin-Lehner	2- 5+ 59-	Signs for the Atkin-Lehner involutions
Class	4720c	Isogeny class
Conductor	4720	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	6962000 = 24 · 53 · 592	Discriminant
Eigenvalues	2- -2 5+ -2 -4  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-61,114]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	1594753024/435125	j-invariant
L	2.0921131698006	L(r)(E,1)/r!
Ω	2.2041080334873	Real period
R	1.8983762483643	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	1180a1 18880o1 42480bt1 23600v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4720c1

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

---

Quadratic twists for elliptic curve 4720c1

-4	8	-3	5
1180a1	18880o1	42480bt1	23600v1

---

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