Cremona's table of elliptic curves

19488 = 2⁵ · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	19488f	Isogeny class
Conductor	19488	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	10467745344 = 26 · 34 · 74 · 292	Discriminant
Eigenvalues	2- 3+ -2 7- -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-974,-10296]	[a1,a2,a3,a4,a6]
Generators	[-20:28:1] [-14:20:1]	Generators of the group modulo torsion
j	1598329885888/163558521	j-invariant
L	5.8589470768323	L(r)(E,1)/r!
Ω	0.86016336037826	Real period
R	3.4057176501083	Regulator
r	2	Rank of the group of rational points
S	0.99999999999981	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19488g1 38976bu2 58464m1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 19488f1

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
-	+	-2	-	-4	-2	2	-4	-8	-	-4	-10	-6	-4	-4	6	-8	-2	0	0	-14	4	-8	10	10

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Quadratic twists for elliptic curve 19488f1

-4	8	-3
19488g1	38976bu2	58464m1

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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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