Cremona's table of elliptic curves

817 = 19 · 43

Field	Data	Notes
Atkin-Lehner	19+ 43-	Signs for the Atkin-Lehner involutions
Class	817a	Isogeny class
Conductor	817	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	56	Modular degree for the optimal curve
Δ	-15523 = -1 · 192 · 43	Discriminant
Eigenvalues	0 -2 -2 -4 -5 -3 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,1,6]	[a1,a2,a3,a4,a6]
Generators	[-2:0:1] [4:9:1]	Generators of the group modulo torsion
j	32768/15523	j-invariant
L	1.5664703894218	L(r)(E,1)/r!
Ω	3.0564514640021	Real period
R	0.25625638225768	Regulator
r	2	Rank of the group of rational points
S	0.99999999999941	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13072g1 52288d1 7353g1 20425a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 817a1

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
0	-2	-2	-4	-5	-3	-3	+	3	-4	-3	-8	-5	-	8	-7	-4	2	7	4	-10	-4	3	-16	1

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Quadratic twists for elliptic curve 817a1

-4	8	-3	5	-7	-11	-19	-43
13072g1	52288d1	7353g1	20425a1	40033c1	98857c1	15523c1	35131d1

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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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