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	32	Product of Tamagawa factors cp
Δ	-514308644610048 = -1 · 213 · 32 · 178	Discriminant
Eigenvalues	2- 3+ -2  0  4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-26304,1980288]	[a1,a2,a3,a4,a6]
Generators	[-174:1122:1]	Generators of the group modulo torsion
j	-491411892194497/125563633938	j-invariant
L	1.90101848041	L(r)(E,1)/r!
Ω	0.49674092925301	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	102b6 3264bc6 2448n6 20400cx6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 816h6

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 816h6

-4	8	-3	5	-7	-11	17
102b6	3264bc6	2448n6	20400cx6	39984df5	98736bz5	13872bi6

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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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