Cremona's table of elliptic curves

4664 = 2³ · 11 · 53

Field	Data	Notes
Atkin-Lehner	2+ 11+ 53+	Signs for the Atkin-Lehner involutions
Class	4664a	Isogeny class
Conductor	4664	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-6566912 = -1 · 210 · 112 · 53	Discriminant
Eigenvalues	2+ -1  0  2 11+ -3  7  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-808,9116]	[a1,a2,a3,a4,a6]
Generators	[10:44:1]	Generators of the group modulo torsion
j	-57042062500/6413	j-invariant
L	3.2093247562352	L(r)(E,1)/r!
Ω	2.2801728946587	Real period
R	0.35187296144878	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	9328d1 37312n1 41976g1 116600p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4664a1

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	2	+	-3	7	3	-5	-3	0	7	-4	-4	4	+	0	8	-4	-3	0	-11	3	18	-19

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Quadratic twists for elliptic curve 4664a1

-4	8	-3	5	-11
9328d1	37312n1	41976g1	116600p1	51304d1

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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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