Cremona's table of elliptic curves

21648 = 2⁴ · 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 41+	Signs for the Atkin-Lehner involutions
Class	21648r	Isogeny class
Conductor	21648	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-522730973794664448 = -1 · 221 · 36 · 112 · 414	Discriminant
Eigenvalues	2- 3+  0  2 11-  0  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-122728,38562160]	[a1,a2,a3,a4,a6]
Generators	[868:24192:1]	Generators of the group modulo torsion
j	-49911230110731625/127619866649088	j-invariant
L	4.8744813893917	L(r)(E,1)/r!
Ω	0.25905901568617	Real period
R	2.3520130039099	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	2706d2 86592cq2 64944bd2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21648r2

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

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Quadratic twists for elliptic curve 21648r2

-4	8	-3
2706d2	86592cq2	64944bd2

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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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