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	21648bc	Isogeny class
Conductor	21648	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-46980152930304 = -1 · 212 · 32 · 11 · 415	Discriminant
Eigenvalues	2- 3-  3  1 11+ -2  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-184,-329836]	[a1,a2,a3,a4,a6]
Generators	[70:72:1]	Generators of the group modulo torsion
j	-169112377/11469763899	j-invariant
L	7.9338280291387	L(r)(E,1)/r!
Ω	0.29103142403275	Real period
R	3.4076337527412	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1353a1 86592ck1 64944bw1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21648bc1

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
-	-	3	1	+	-2	3	-5	-3	-1	-7	1	+	-10	2	-4	-1	6	-6	-10	6	4	-12	-6	12

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Quadratic twists for elliptic curve 21648bc1

-4	8	-3
1353a1	86592ck1	64944bw1

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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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