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	21216k	Isogeny class
Conductor	21216	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	321024	Modular degree for the optimal curve
Δ	1275191700526156608 = 26 · 322 · 133 · 172	Discriminant
Eigenvalues	2- 3+  2  0  2 13+ 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1006762,385331908]	[a1,a2,a3,a4,a6]
Generators	[93192:7385633:512]	Generators of the group modulo torsion
j	1763293530283953913792/19924870320721197	j-invariant
L	5.1264757411722	L(r)(E,1)/r!
Ω	0.27322026664608	Real period
R	9.3815802980181	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	21216n1 42432cr2 63648b1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21216k1

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	2	+	-	-6	4	-6	0	8	-2	-8	-4	2	12	10	-2	10	12	-16	0	0	-8

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Quadratic twists for elliptic curve 21216k1

-4	8	-3
21216n1	42432cr2	63648b1

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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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