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	21216f	Isogeny class
Conductor	21216	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	2517023808 = 26 · 34 · 134 · 17	Discriminant
Eigenvalues	2+ 3-  4 -2  4 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-346,-688]	[a1,a2,a3,a4,a6]
j	71783828416/39328497	j-invariant
L	4.7300369834161	L(r)(E,1)/r!
Ω	1.182509245854	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21216j1 42432i1 63648s1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21216f1

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

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Quadratic twists for elliptic curve 21216f1

-4	8	-3
21216j1	42432i1	63648s1

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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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