Cremona's table of elliptic curves

4161 = 3 · 19 · 73

Field	Data	Notes
Atkin-Lehner	3+ 19+ 73+	Signs for the Atkin-Lehner involutions
Class	4161a	Isogeny class
Conductor	4161	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	163894967070987 = 3 · 192 · 736	Discriminant
Eigenvalues	1 3+  0 -2  4  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13880,-135447]	[a1,a2,a3,a4,a6]
Generators	[-1772:31485:64]	Generators of the group modulo torsion
j	295761063348159625/163894967070987	j-invariant
L	3.5778725833533	L(r)(E,1)/r!
Ω	0.47126097276074	Real period
R	7.5921257862568	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	66576ba2 12483e2 104025m2 79059j2	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4161a2

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	4	2	-4	+	8	-8	6	6	6	-10	0	4	-8	2	8	0	+	-8	0	-6	-10

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Quadratic twists for elliptic curve 4161a2

-4	-3	5	-19
66576ba2	12483e2	104025m2	79059j2

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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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