Cremona's table of elliptic curves

205 = 5 · 41

Field	Data	Notes
Atkin-Lehner	5+ 41-	Signs for the Atkin-Lehner involutions
Class	205b	Isogeny class
Conductor	205	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	1025 = 52 · 41	Discriminant
Eigenvalues	-1  2 5+  2  6  2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-21,-46]	[a1,a2,a3,a4,a6]
j	1027243729/1025	j-invariant
L	1.1148927568821	L(r)(E,1)/r!
Ω	2.2297855137643	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	3280i1 13120t1 1845f1 1025c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205b1

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
-1	2	+	2	6	2	2	-6	-4	10	0	-6	-	-4	-2	-14	12	-10	-2	-2	6	-2	0	10	10

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Quadratic twists for elliptic curve 205b1

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280i1	13120t1	1845f1	1025c1	10045j1	24805a1	34645h1	59245c1	74005f1	108445i1	8405a1

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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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