Cremona's table of elliptic curves

11552 = 2⁵ · 19²

Field	Data	Notes
Atkin-Lehner	2- 19+	Signs for the Atkin-Lehner involutions
Class	11552r	Isogeny class
Conductor	11552	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	38304	Modular degree for the optimal curve
Δ	-8695584276992 = -1 · 29 · 198	Discriminant
Eigenvalues	2- -3  2  2  3  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6859,-260642]	[a1,a2,a3,a4,a6]
j	-4104	j-invariant
L	1.553841283312	L(r)(E,1)/r!
Ω	0.25897354721867	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	11552d1 23104f1 103968p1 11552l1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 11552r1

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	2	3	2	-6	+	4	-6	8	-8	-3	8	-10	2	3	14	-7	2	11	4	15	-18	-3

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Quadratic twists for elliptic curve 11552r1

-4	8	-3	-19
11552d1	23104f1	103968p1	11552l1

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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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