Cremona's table of elliptic curves

472 = 2³ · 59

Field	Data	Notes
Atkin-Lehner	2- 59+	Signs for the Atkin-Lehner involutions
Class	472d	Isogeny class
Conductor	472	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-60416 = -1 · 210 · 59	Discriminant
Eigenvalues	2-  3 -3  3  6 -6 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19,-34]	[a1,a2,a3,a4,a6]
j	-740772/59	j-invariant
L	2.2763188894943	L(r)(E,1)/r!
Ω	1.1381594447471	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	944e1 3776k1 4248d1 11800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 472d1

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
-	3	-3	3	6	-6	-2	-1	8	-1	-2	-4	-1	-10	6	5	+	-8	2	-4	-8	-11	-10	-16	-4

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Quadratic twists for elliptic curve 472d1

-4	8	-3	5	-7	-11	13	-59
944e1	3776k1	4248d1	11800b1	23128u1	57112c1	79768g1	27848e1

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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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