Cremona's table of elliptic curves

16368 = 2⁴ · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 31-	Signs for the Atkin-Lehner involutions
Class	16368p	Isogeny class
Conductor	16368	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-1072693248 = -1 · 220 · 3 · 11 · 31	Discriminant
Eigenvalues	2- 3+ -2 -4 11+  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,256,0]	[a1,a2,a3,a4,a6]
Generators	[1:16:1]	Generators of the group modulo torsion
j	451217663/261888	j-invariant
L	2.6151471458141	L(r)(E,1)/r!
Ω	0.93377183755623	Real period
R	2.8006275630011	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	2046i1 65472cs1 49104bu1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 16368p1

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	0	0	-2	-	-2	-6	-4	-4	10	0	2	-12	4	14	8	12	-18	18

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Quadratic twists for elliptic curve 16368p1

-4	8	-3
2046i1	65472cs1	49104bu1

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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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