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	4664b	Isogeny class
Conductor	4664	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-7910144 = -1 · 28 · 11 · 532	Discriminant
Eigenvalues	2+ -1  3 -4 11+  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-129,-539]	[a1,a2,a3,a4,a6]
Generators	[25:106:1]	Generators of the group modulo torsion
j	-934577152/30899	j-invariant
L	3.34061709463	L(r)(E,1)/r!
Ω	0.70647680154173	Real period
R	0.59106984959377	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	9328e1 37312q1 41976h1 116600q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4664b1

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	3	-4	+	6	-2	0	-5	6	3	-5	2	-4	4	+	-9	-10	5	9	12	-14	-6	-9	-19

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Quadratic twists for elliptic curve 4664b1

-4	8	-3	5	-11
9328e1	37312q1	41976h1	116600q1	51304e1

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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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