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	1050625 = 54 · 412	Discriminant
Eigenvalues	-1  0 5- -4  0 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-27,26]	[a1,a2,a3,a4,a6]
Generators	[-4:9:1]	Generators of the group modulo torsion
j	2102071041/1050625	j-invariant
L	0.98123969640841	L(r)(E,1)/r!
Ω	2.4491172865478	Real period
R	0.80130069866235	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3280m2 13120l2 1845c2 1025b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205a2

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 205a2

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280m2	13120l2	1845c2	1025b2	10045d2	24805c2	34645b2	59245a2	74005p2	108445e2	8405c2

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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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