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	4720a	Isogeny class
Conductor	4720	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-14750000 = -1 · 24 · 56 · 59	Discriminant
Eigenvalues	2+  0 5-  0  0  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22,-189]	[a1,a2,a3,a4,a6]
Generators	[11:30:1]	Generators of the group modulo torsion
j	-73598976/921875	j-invariant
L	3.8545616456877	L(r)(E,1)/r!
Ω	0.94682696962132	Real period
R	2.7140204559441	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	2360a1 18880g1 42480c1 23600e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4720a1

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	0	0	-2	4	-2	2	-4	-4	-10	10	6	-10	-	10	-2	-8	4	8	-14	-10	-16

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Quadratic twists for elliptic curve 4720a1

-4	8	-3	5
2360a1	18880g1	42480c1	23600e1

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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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