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	-70644025 = -1 · 52 · 414	Discriminant
Eigenvalues	-1  0 5- -4  0 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,98,126]	[a1,a2,a3,a4,a6]
Generators	[1:14:1]	Generators of the group modulo torsion
j	105087226959/70644025	j-invariant
L	0.98123969640841	L(r)(E,1)/r!
Ω	1.2245586432739	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	3280m4 13120l4 1845c4 1025b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205a4

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 205a4

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280m4	13120l4	1845c4	1025b4	10045d4	24805c3	34645b3	59245a3	74005p3	108445e3	8405c4

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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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