Cremona's table of elliptic curves

442 = 2 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	442d	Isogeny class
Conductor	442	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	7514 = 2 · 13 · 172	Discriminant
Eigenvalues	2-  2 -2  2  4 13+ 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-139,-689]	[a1,a2,a3,a4,a6]
j	297141543217/7514	j-invariant
L	2.7807390608133	L(r)(E,1)/r!
Ω	1.3903695304067	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3536g2 14144h2 3978c2 11050j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 442d2

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	-2	2	4	+	+	-4	8	-8	10	-10	-8	-12	8	2	12	0	-4	-6	-4	-4	12	-2	12

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Quadratic twists for elliptic curve 442d2

-4	8	-3	5	-7	-11	13	17
3536g2	14144h2	3978c2	11050j2	21658bf2	53482f2	5746c2	7514g2

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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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