Cremona's table of elliptic curves

4264 = 2³ · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 13- 41-	Signs for the Atkin-Lehner involutions
Class	4264a	Isogeny class
Conductor	4264	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	-545792 = -1 · 210 · 13 · 41	Discriminant
Eigenvalues	2+  1  2  2 -6 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,8,-32]	[a1,a2,a3,a4,a6]
Generators	[12:44:1]	Generators of the group modulo torsion
j	48668/533	j-invariant
L	4.6990635865567	L(r)(E,1)/r!
Ω	1.4381790718927	Real period
R	1.6336851503382	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	8528a1 34112a1 38376t1 106600h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4264a1

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	2	2	-6	-	0	-4	0	-10	1	-8	-	10	2	-6	-3	-7	-2	0	14	4	-3	-5	-3

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Quadratic twists for elliptic curve 4264a1

-4	8	-3	5	13
8528a1	34112a1	38376t1	106600h1	55432b1

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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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