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	2050c	Isogeny class
Conductor	2050	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	4100000000 = 28 · 58 · 41	Discriminant
Eigenvalues	2+  2 5+  2  2  6  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-400,0]	[a1,a2,a3,a4,a6]
j	454756609/262400	j-invariant
L	2.3616918247746	L(r)(E,1)/r!
Ω	1.1808459123873	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	16400v1 65600x1 18450bm1 410d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2050c1

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	6	6	-2	4	-6	0	-10	-	-4	-2	6	12	-10	-2	10	10	-6	0	10	-2

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Quadratic twists for elliptic curve 2050c1

-4	8	-3	5	-7	41
16400v1	65600x1	18450bm1	410d1	100450n1	84050d1

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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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