Cremona's table of elliptic curves

21216 = 2⁵ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	21216l	Isogeny class
Conductor	21216	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	5003241984 = 29 · 32 · 13 · 174	Discriminant
Eigenvalues	2- 3+ -2  0 -4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1344,-18216]	[a1,a2,a3,a4,a6]
Generators	[-19:10:1] [45:102:1]	Generators of the group modulo torsion
j	524776831496/9771957	j-invariant
L	5.9239748255896	L(r)(E,1)/r!
Ω	0.78933954320514	Real period
R	3.752488315444	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21216p3 42432cf3 63648k3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21216l3

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

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Quadratic twists for elliptic curve 21216l3

-4	8	-3
21216p3	42432cf3	63648k3

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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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