Cremona's table of elliptic curves

19392 = 2⁶ · 3 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 101-	Signs for the Atkin-Lehner involutions
Class	19392h	Isogeny class
Conductor	19392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	4712256 = 26 · 36 · 101	Discriminant
Eigenvalues	2+ 3+ -1 -4 -4 -1 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-111,477]	[a1,a2,a3,a4,a6]
Generators	[4:9:1] [12:27:1]	Generators of the group modulo torsion
j	2384621056/73629	j-invariant
L	5.4797303227005	L(r)(E,1)/r!
Ω	2.4284594757693	Real period
R	1.1282317817895	Regulator
r	2	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19392s1 9696h1 58176i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19392h1

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	-4	-4	-1	-3	5	7	0	-5	-6	-12	-4	-7	8	-12	-10	-2	3	-10	3	16	-18	-2

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Quadratic twists for elliptic curve 19392h1

-4	8	-3
19392s1	9696h1	58176i1

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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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