Cremona's table of elliptic curves

4205 = 5 · 29²

Field	Data	Notes
Atkin-Lehner	5+ 29+	Signs for the Atkin-Lehner involutions
Class	4205a	Isogeny class
Conductor	4205	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-12506160324025 = -1 · 52 · 298	Discriminant
Eigenvalues	1  0 5+ -2  6  2  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1945,166426]	[a1,a2,a3,a4,a6]
Generators	[18:446:1]	Generators of the group modulo torsion
j	1367631/21025	j-invariant
L	3.927848505007	L(r)(E,1)/r!
Ω	0.5284498526891	Real period
R	3.7163871699646	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67280l2 37845j2 21025a2 145a2	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 4205a2

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	+	-2	6	2	2	2	2	+	-2	-10	-2	-8	12	-6	-8	6	2	-12	6	10	-14	-18	-2

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Quadratic twists for elliptic curve 4205a2

-4	-3	5	29
67280l2	37845j2	21025a2	145a2

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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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