Cremona's table of elliptic curves

205 = 5 · 41

Field	Data	Notes
Atkin-Lehner	5+ 41-	Signs for the Atkin-Lehner involutions
Class	205b	Isogeny class
Conductor	205	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1050625 = -1 · 54 · 412	Discriminant
Eigenvalues	-1  2 5+  2  6  2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-16,-62]	[a1,a2,a3,a4,a6]
j	-454756609/1050625	j-invariant
L	1.1148927568821	L(r)(E,1)/r!
Ω	1.1148927568821	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	3280i2 13120t2 1845f2 1025c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 205b2

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

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Quadratic twists for elliptic curve 205b2

-4	8	-3	5	-7	-11	13	17	-19	-23	41
3280i2	13120t2	1845f2	1025c2	10045j2	24805a2	34645h2	59245c2	74005f2	108445i2	8405a2

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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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