Cremona's table of elliptic curves

2050 = 2 · 5² · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 41+	Signs for the Atkin-Lehner involutions
Class	2050d	Isogeny class
Conductor	2050	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	110273600000000 = 212 · 58 · 413	Discriminant
Eigenvalues	2-  2 5+ -2  0  4  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-38563,-2886719]	[a1,a2,a3,a4,a6]
j	405897921250921/7057510400	j-invariant
L	4.0925706460215	L(r)(E,1)/r!
Ω	0.34104755383513	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	16400o3 65600l3 18450n3 410c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2050d3

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

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Quadratic twists for elliptic curve 2050d3

-4	8	-3	5	-7	41
16400o3	65600l3	18450n3	410c3	100450by3	84050l3

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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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