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	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	11492 = 22 · 132 · 17	Discriminant
Eigenvalues	2-  2 -2  2  4 13+ 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-9,-13]	[a1,a2,a3,a4,a6]
j	81182737/11492	j-invariant
L	2.7807390608133	L(r)(E,1)/r!
Ω	2.7807390608133	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3536g1 14144h1 3978c1 11050j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 442d1

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 442d1

-4	8	-3	5	-7	-11	13	17
3536g1	14144h1	3978c1	11050j1	21658bf1	53482f1	5746c1	7514g1

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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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