Cremona's table of elliptic curves

5491 = 17² · 19

Field	Data	Notes
Atkin-Lehner	17+ 19-	Signs for the Atkin-Lehner involutions
Class	5491b	Isogeny class
Conductor	5491	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-651166029845027 = -1 · 1711 · 19	Discriminant
Eigenvalues	0 -3  2 -4  2  6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-13294,1362129]	[a1,a2,a3,a4,a6]
j	-10764582912/26977283	j-invariant
L	0.90518899170225	L(r)(E,1)/r!
Ω	0.45259449585112	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	87856n1 49419e1 323a1 104329c1	Quadratic twists by: -4 -3 17 -19

Hecke Eigenvalues for elliptic curve 5491b1

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	-3	2	-4	2	6	+	-	0	9	9	-2	6	-1	-3	2	14	6	-14	-16	2	-8	-3	2	7

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Quadratic twists for elliptic curve 5491b1

-4	-3	17	-19
87856n1	49419e1	323a1	104329c1

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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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