Cremona's table of elliptic curves

3553 = 11 · 17 · 19

Field	Data	Notes
Atkin-Lehner	11+ 17+ 19+	Signs for the Atkin-Lehner involutions
Class	3553a	Isogeny class
Conductor	3553	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	176	Modular degree for the optimal curve
Δ	-39083 = -1 · 112 · 17 · 19	Discriminant
Eigenvalues	0 -1 -2 -2 11+  4 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,1,9]	[a1,a2,a3,a4,a6]
Generators	[3:5:1]	Generators of the group modulo torsion
j	32768/39083	j-invariant
L	1.7675333220002	L(r)(E,1)/r!
Ω	2.8459266312681	Real period
R	0.31053740152335	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	56848j1 31977u1 88825d1 39083h1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3553a1

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	-1	-2	-2	+	4	+	+	6	-3	3	6	-6	9	1	12	-10	-2	6	12	-2	0	-17	-4	9

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Quadratic twists for elliptic curve 3553a1

-4	-3	5	-11	17	-19
56848j1	31977u1	88825d1	39083h1	60401h1	67507c1

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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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