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	442b	Isogeny class
Conductor	442	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	212556032 = 28 · 132 · 173	Discriminant
Eigenvalues	2-  0 -4 -2 -2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-172,-465]	[a1,a2,a3,a4,a6]
Generators	[-9:21:1]	Generators of the group modulo torsion
j	559679941521/212556032	j-invariant
L	2.1459321166619	L(r)(E,1)/r!
Ω	1.3616952016008	Real period
R	0.13132724282076	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3536j1 14144k1 3978b1 11050d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 442b1

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
-	0	-4	-2	-2	+	-	0	-4	2	-2	0	0	4	-8	-6	8	-2	16	-14	-16	8	-12	-18	-4

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Quadratic twists for elliptic curve 442b1

-4	8	-3	5	-7	-11	13	17
3536j1	14144k1	3978b1	11050d1	21658x1	53482c1	5746g1	7514f1

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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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