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	2050a	Isogeny class
Conductor	2050	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-1103812890625000000 = -1 · 26 · 514 · 414	Discriminant
Eigenvalues	2+  0 5+ -4  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-538667,-160211259]	[a1,a2,a3,a4,a6]
j	-1106280483969259521/70644025000000	j-invariant
L	0.70231006298444	L(r)(E,1)/r!
Ω	0.087788757873055	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	16400r4 65600s3 18450br4 410b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2050a4

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	0	2	-2	0	0	-2	0	-6	-	4	12	10	-4	-2	8	-4	6	4	4	10	-18

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Quadratic twists for elliptic curve 2050a4

-4	8	-3	5	-7	41
16400r4	65600s3	18450br4	410b4	100450e3	84050a3

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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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