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	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	160156250000 = 24 · 512 · 41	Discriminant
Eigenvalues	2-  2 5+ -2  0  4  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4188,100781]	[a1,a2,a3,a4,a6]
j	519912412921/10250000	j-invariant
L	4.0925706460215	L(r)(E,1)/r!
Ω	1.0231426615054	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	16400o1 65600l1 18450n1 410c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2050d1

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 2050d1

-4	8	-3	5	-7	41
16400o1	65600l1	18450n1	410c1	100450by1	84050l1

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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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