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	3553c	Isogeny class
Conductor	3553	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-119729942651 = -1 · 11 · 174 · 194	Discriminant
Eigenvalues	-2 -1 -3  2 11-  4 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-74002,7773160]	[a1,a2,a3,a4,a6]
Generators	[283:3068:1]	Generators of the group modulo torsion
j	-44818771954214268928/119729942651	j-invariant
L	1.2333756023305	L(r)(E,1)/r!
Ω	0.90943119579488	Real period
R	0.16952568924861	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	56848g1 31977k1 88825i1 39083e1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3553c1

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
-2	-1	-3	2	-	4	-	+	-5	-8	-1	3	0	-6	8	10	-15	8	13	5	0	14	-2	-5	1

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Quadratic twists for elliptic curve 3553c1

-4	-3	5	-11	17	-19
56848g1	31977k1	88825i1	39083e1	60401a1	67507k1

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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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