Cremona's table of elliptic curves

816 = 2⁴ · 3 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 17-	Signs for the Atkin-Lehner involutions
Class	816h	Isogeny class
Conductor	816	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	1443889152 = 220 · 34 · 17	Discriminant
Eigenvalues	2- 3+ -2  0  4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-544,-4352]	[a1,a2,a3,a4,a6]
Generators	[-14:18:1]	Generators of the group modulo torsion
j	4354703137/352512	j-invariant
L	1.90101848041	L(r)(E,1)/r!
Ω	0.99348185850601	Real period
R	0.95674544237212	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	102b1 3264bc1 2448n1 20400cx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 816h1

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

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Quadratic twists for elliptic curve 816h1

-4	8	-3	5	-7	-11	17
102b1	3264bc1	2448n1	20400cx1	39984df1	98736bz1	13872bi1

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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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