Cremona's table of elliptic curves

477 = 3² · 53

Field	Data	Notes
Atkin-Lehner	3- 53-	Signs for the Atkin-Lehner involutions
Class	477a	Isogeny class
Conductor	477	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	28	Modular degree for the optimal curve
Δ	-38637 = -1 · 36 · 53	Discriminant
Eigenvalues	1 3-  0 -4  0 -3  3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,3,-10]	[a1,a2,a3,a4,a6]
Generators	[2:0:1]	Generators of the group modulo torsion
j	3375/53	j-invariant
L	2.1819346902216	L(r)(E,1)/r!
Ω	1.7789208762302	Real period
R	1.2265496005901	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7632l1 30528f1 53a1 11925p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 477a1

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
1	-	0	-4	0	-3	3	-5	-7	7	4	5	-6	-2	2	-	2	-8	-12	-1	-4	-1	1	14	1

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Quadratic twists for elliptic curve 477a1

-4	8	-3	5	-7	-11	13	53
7632l1	30528f1	53a1	11925p1	23373f1	57717w1	80613j1	25281e1

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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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