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	4720b	Isogeny class
Conductor	4720	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8448	Modular degree for the optimal curve
Δ	-1051540480000 = -1 · 213 · 54 · 593	Discriminant
Eigenvalues	2-  2 5+ -5  3 -1  3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2504,-11280]	[a1,a2,a3,a4,a6]
j	423733973831/256723750	j-invariant
L	2.031259594056	L(r)(E,1)/r!
Ω	0.50781489851399	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	590a1 18880r1 42480cc1 23600n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4720b1

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	+	-5	3	-1	3	4	0	0	-8	11	-3	1	-6	12	+	2	4	3	2	1	3	6	2

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Quadratic twists for elliptic curve 4720b1

-4	8	-3	5
590a1	18880r1	42480cc1	23600n1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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