Cremona's table of elliptic curves

18496 = 2⁶ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	18496a	Isogeny class
Conductor	18496	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-228581619826688 = -1 · 215 · 178	Discriminant
Eigenvalues	2+  0  0  2 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5780,707472]	[a1,a2,a3,a4,a6]
Generators	[608:15132:1]	Generators of the group modulo torsion
j	27000/289	j-invariant
L	4.7816348048383	L(r)(E,1)/r!
Ω	0.4110989207926	Real period
R	5.815674236774	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	18496b2 9248a2 1088b2	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 18496a2

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

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Quadratic twists for elliptic curve 18496a2

-4	8	17
18496b2	9248a2	1088b2

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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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