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	3553b	Isogeny class
Conductor	3553	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	528	Modular degree for the optimal curve
Δ	742577 = 112 · 17 · 192	Discriminant
Eigenvalues	1  2 -2  4 11+ -2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-36,59]	[a1,a2,a3,a4,a6]
Generators	[-2:67:8]	Generators of the group modulo torsion
j	5386984777/742577	j-invariant
L	5.4393303700171	L(r)(E,1)/r!
Ω	2.7375082208511	Real period
R	1.9869640312262	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	56848k1 31977w1 88825f1 39083i1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3553b1

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

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Quadratic twists for elliptic curve 3553b1

-4	-3	5	-11	17	-19
56848k1	31977w1	88825f1	39083i1	60401i1	67507f1

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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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