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	2050f	Isogeny class
Conductor	2050	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	1025000000 = 26 · 58 · 41	Discriminant
Eigenvalues	2-  0 5+  2 -6  2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-355,2147]	[a1,a2,a3,a4,a6]
Generators	[-1:50:1]	Generators of the group modulo torsion
j	315821241/65600	j-invariant
L	4.2330031704034	L(r)(E,1)/r!
Ω	1.4743338947476	Real period
R	0.47852154177147	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	16400q1 65600o1 18450j1 410a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2050f1

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

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Quadratic twists for elliptic curve 2050f1

-4	8	-3	5	-7	41
16400q1	65600o1	18450j1	410a1	100450bh1	84050g1

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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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