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	16	Product of Tamagawa factors cp
Δ	21307392 = 213 · 32 · 172	Discriminant
Eigenvalues	2- 3+ -2  0  4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-443904,113984640]	[a1,a2,a3,a4,a6]
Generators	[216:5304:1]	Generators of the group modulo torsion
j	2361739090258884097/5202	j-invariant
L	1.90101848041	L(r)(E,1)/r!
Ω	0.99348185850601	Real period
R	1.9134908847442	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	102b5 3264bc5 2448n5 20400cx5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 816h5

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 816h5

-4	8	-3	5	-7	-11	17
102b5	3264bc5	2448n5	20400cx5	39984df6	98736bz6	13872bi5

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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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