Cremona's table of elliptic curves

11552 = 2⁵ · 19²

Field	Data	Notes
Atkin-Lehner	2+ 19+	Signs for the Atkin-Lehner involutions
Class	11552a	Isogeny class
Conductor	11552	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-438976 = -1 · 26 · 193	Discriminant
Eigenvalues	2+  0 -2  0  0  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,19,0]	[a1,a2,a3,a4,a6]
Generators	[9:30:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	3.7276182651362	L(r)(E,1)/r!
Ω	1.7761057400603	Real period
R	2.0987592016957	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	11552a1 23104z2 103968bk1 11552n1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 11552a1

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	-2	0	0	4	-2	+	0	4	0	12	-8	0	0	4	0	-10	0	0	6	0	0	16	8

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Quadratic twists for elliptic curve 11552a1

-4	8	-3	-19
11552a1	23104z2	103968bk1	11552n1

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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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