Cremona's table of elliptic curves

4335 = 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	3- 5- 17+	Signs for the Atkin-Lehner involutions
Class	4335f	Isogeny class
Conductor	4335	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	117045 = 34 · 5 · 172	Discriminant
Eigenvalues	0 3- 5- -2 -5  4 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-45,101]	[a1,a2,a3,a4,a6]
Generators	[3:1:1]	Generators of the group modulo torsion
j	35651584/405	j-invariant
L	3.6034626455428	L(r)(E,1)/r!
Ω	3.3337844143452	Real period
R	0.27022313065874	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360cu1 13005h1 21675b1 4335a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4335f1

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
0	-	-	-2	-5	4	+	5	-8	-5	8	6	-5	6	2	-14	-9	-5	10	7	-10	-15	2	1	-6

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Quadratic twists for elliptic curve 4335f1

-4	-3	5	17
69360cu1	13005h1	21675b1	4335a1

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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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