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
deg	5760	Modular degree for the optimal curve
Δ	456273760113 = 32 · 194 · 733	Discriminant
Eigenvalues	1 3+  0 -2  4  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-8465,294504]	[a1,a2,a3,a4,a6]
Generators	[40:128:1]	Generators of the group modulo torsion
j	67094166273513625/456273760113	j-invariant
L	3.5778725833533	L(r)(E,1)/r!
Ω	0.94252194552149	Real period
R	3.7960628931284	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	66576ba1 12483e1 104025m1 79059j1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4161a1

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 4161a1

-4	-3	5	-19
66576ba1	12483e1	104025m1	79059j1

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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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