Cremona's table of elliptic curves

53664 = 2⁵ · 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 43+	Signs for the Atkin-Lehner involutions
Class	53664a	Isogeny class
Conductor	53664	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	15872	Modular degree for the optimal curve
Δ	-4615104 = -1 · 26 · 3 · 13 · 432	Discriminant
Eigenvalues	2+ 3+  2 -4  4 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,38,40]	[a1,a2,a3,a4,a6]
Generators	[10:75:8]	Generators of the group modulo torsion
j	92345408/72111	j-invariant
L	5.3119922403565	L(r)(E,1)/r!
Ω	1.5704228473271	Real period
R	3.3825235345428	Regulator
r	1	Rank of the group of rational points
S	1.0000000000167	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53664l1 107328bi2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 53664a1

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	-4	4	+	6	-8	6	8	-10	-8	6	+	8	-6	-12	-6	-10	0	-4	16	8	10	10

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Quadratic twists for elliptic curve 53664a1

-4	8
53664l1	107328bi2

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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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