Cremona's table of elliptic curves

18496 = 2⁶ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	18496c	Isogeny class
Conductor	18496	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-528480705039302656 = -1 · 218 · 1710	Discriminant
Eigenvalues	2+  0 -2 -4  0  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12716,-34980560]	[a1,a2,a3,a4,a6]
Generators	[376:3660:1]	Generators of the group modulo torsion
j	-35937/83521	j-invariant
L	3.0371728240595	L(r)(E,1)/r!
Ω	0.13266099441832	Real period
R	5.7235603377176	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	18496j4 289a4 1088e4	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 18496c4

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

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Quadratic twists for elliptic curve 18496c4

-4	8	17
18496j4	289a4	1088e4

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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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