Cremona's table of elliptic curves

205 = 5 · 41

Field	Data	Notes
Atkin-Lehner	5- 41-	Signs for the Atkin-Lehner involutions
Class	205a	Isogeny class
Conductor	205	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	16015625 = 58 · 41	Discriminant
Eigenvalues	-1  0 5- -4  0 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-232,-1286]	[a1,a2,a3,a4,a6]
Generators	[-8:6:1]	Generators of the group modulo torsion
j	1375407924561/16015625	j-invariant
L	0.98123969640841	L(r)(E,1)/r!
Ω	1.2245586432739	Real period
R	0.40065034933118	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	3280m3 13120l3 1845c3 1025b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205a3

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	0	-	-4	0	-2	-6	0	-8	6	0	6	-	4	-4	6	-4	14	-8	-12	-6	-4	4	-6	-6

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Quadratic twists for elliptic curve 205a3

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280m3	13120l3	1845c3	1025b3	10045d3	24805c4	34645b4	59245a4	74005p4	108445e4	8405c3

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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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