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
Δ	8405 = 5 · 412	Discriminant
Eigenvalues	1  2 5-  2  0 -4  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-27,44]	[a1,a2,a3,a4,a6]
j	2305199161/8405	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	3280k2 13120e2 1845d2 1025a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205c2

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 205c2

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280k2	13120e2	1845d2	1025a2	10045h2	24805g2	34645c2	59245b2	74005u2	108445c2	8405b2

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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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