Cremona's table of elliptic curves

4165 = 5 · 7² · 17

Field	Data	Notes
Atkin-Lehner	5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	4165j	Isogeny class
Conductor	4165	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-21250350625 = -1 · 54 · 76 · 172	Discriminant
Eigenvalues	1 -2 5- 7-  2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-173,7053]	[a1,a2,a3,a4,a6]
Generators	[-1:85:1]	Generators of the group modulo torsion
j	-4826809/180625	j-invariant
L	3.2072490195292	L(r)(E,1)/r!
Ω	1.0076264198025	Real period
R	0.79574358028392	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	66640cf2 37485bd2 20825s2 85a2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4165j2

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	-2	+	0	6	-6	10	2	-10	4	-12	-10	-8	14	8	-2	14	-14	-4	-6	-2

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Quadratic twists for elliptic curve 4165j2

-4	-3	5	-7	17
66640cf2	37485bd2	20825s2	85a2	70805l2

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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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