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	19392bd	Isogeny class
Conductor	19392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	58176 = 26 · 32 · 101	Discriminant
Eigenvalues	2- 3+  3  0 -4  3 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-19,37]	[a1,a2,a3,a4,a6]
Generators	[4:3:1]	Generators of the group modulo torsion
j	12487168/909	j-invariant
L	5.1940590774892	L(r)(E,1)/r!
Ω	3.4477047245621	Real period
R	0.75326332914849	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	19392bo1 9696i1 58176bz1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19392bd1

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	0	-4	3	-3	-1	1	0	5	2	-4	-4	-1	0	0	14	-14	-3	-14	5	-4	18	-10

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Quadratic twists for elliptic curve 19392bd1

-4	8	-3
19392bo1	9696i1	58176bz1

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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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