Cremona's table of elliptic curves

205 = 5 · 41

Field	Data	Notes
Atkin-Lehner	5- 41+	Signs for the Atkin-Lehner involutions
Class	205c	Isogeny class
Conductor	205	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	1025 = 52 · 41	Discriminant
Eigenvalues	1  2 5-  2  0 -4  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,-1]	[a1,a2,a3,a4,a6]
j	1771561/1025	j-invariant
L	2.0770346319911	L(r)(E,1)/r!
Ω	4.1540692639822	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	3280k1 13120e1 1845d1 1025a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205c1

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	0	-4	4	0	-8	2	0	-6	+	8	2	8	-12	2	10	8	-6	-8	12	14	-8

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Quadratic twists for elliptic curve 205c1

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280k1	13120e1	1845d1	1025a1	10045h1	24805g1	34645c1	59245b1	74005u1	108445c1	8405b1

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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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