Cremona's table of elliptic curves

5491 = 17² · 19

Field	Data	Notes
Atkin-Lehner	17+ 19-	Signs for the Atkin-Lehner involutions
Class	5491d	Isogeny class
Conductor	5491	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1664	Modular degree for the optimal curve
Δ	1773593 = 173 · 192	Discriminant
Eigenvalues	1 -2  4  2  6 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-134,579]	[a1,a2,a3,a4,a6]
j	53582633/361	j-invariant
L	2.661697705981	L(r)(E,1)/r!
Ω	2.661697705981	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	87856j1 49419j1 5491c1 104329e1	Quadratic twists by: -4 -3 17 -19

Hecke Eigenvalues for elliptic curve 5491d1

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
1	-2	4	2	6	-2	+	-	2	0	2	-8	4	-4	8	-6	12	4	4	-6	16	-10	-4	-6	12

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Quadratic twists for elliptic curve 5491d1

-4	-3	17	-19
87856j1	49419j1	5491c1	104329e1

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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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