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	2	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	1025 = 52 · 41	Discriminant
Eigenvalues	-1  0 5- -4  0 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-22,44]	[a1,a2,a3,a4,a6]
Generators	[-1:8:1]	Generators of the group modulo torsion
j	1128111921/1025	j-invariant
L	0.98123969640841	L(r)(E,1)/r!
Ω	4.8982345730957	Real period
R	1.6026013973247	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	3280m1 13120l1 1845c1 1025b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205a1

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 205a1

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280m1	13120l1	1845c1	1025b1	10045d1	24805c1	34645b1	59245a1	74005p1	108445e1	8405c1

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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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