Cremona's table of elliptic curves

4770 = 2 · 3² · 5 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 53-	Signs for the Atkin-Lehner involutions
Class	4770k	Isogeny class
Conductor	4770	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6911193375000 = 23 · 39 · 56 · 532	Discriminant
Eigenvalues	2+ 3- 5+  2  0 -4  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-11610,-461700]	[a1,a2,a3,a4,a6]
Generators	[-69:120:1]	Generators of the group modulo torsion
j	237418132332961/9480375000	j-invariant
L	2.7729566386401	L(r)(E,1)/r!
Ω	0.46106016956551	Real period
R	3.0071526686563	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	38160bp2 1590u2 23850cg2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 4770k2

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

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Quadratic twists for elliptic curve 4770k2

-4	-3	5
38160bp2	1590u2	23850cg2

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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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