Cremona's table of elliptic curves

11552 = 2⁵ · 19²

Field	Data	Notes
Atkin-Lehner	2- 19+	Signs for the Atkin-Lehner involutions
Class	11552s	Isogeny class
Conductor	11552	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-3511808 = -1 · 29 · 193	Discriminant
Eigenvalues	2- -3 -2  3 -6  5  7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3211,-70034]	[a1,a2,a3,a4,a6]
j	-1042590744	j-invariant
L	1.2684385980613	L(r)(E,1)/r!
Ω	0.31710964951533	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11552q1 23104bi1 103968j1 11552e1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 11552s1

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
-	-3	-2	3	-6	5	7	+	3	5	6	6	8	6	0	5	-3	8	9	12	-3	0	-6	2	-8

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Quadratic twists for elliptic curve 11552s1

-4	8	-3	-19
11552q1	23104bi1	103968j1	11552e1

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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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