Cremona's table of elliptic curves

472 = 2³ · 59

Field	Data	Notes
Atkin-Lehner	2+ 59-	Signs for the Atkin-Lehner involutions
Class	472c	Isogeny class
Conductor	472	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-120832 = -1 · 211 · 59	Discriminant
Eigenvalues	2+  2  2  1  1 -1 -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,12]	[a1,a2,a3,a4,a6]
j	24334/59	j-invariant
L	2.310557748397	L(r)(E,1)/r!
Ω	2.310557748397	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	944c1 3776d1 4248h1 11800g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 472c1

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	1	1	-1	-1	0	0	-4	4	3	-3	-1	10	-4	-	-6	4	13	-6	-1	-3	2	-10

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Quadratic twists for elliptic curve 472c1

-4	8	-3	5	-7	-11	13	-59
944c1	3776d1	4248h1	11800g1	23128i1	57112g1	79768k1	27848j1

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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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