Cremona's table of elliptic curves

5491 = 17² · 19

Field	Data	Notes
Atkin-Lehner	17+ 19-	Signs for the Atkin-Lehner involutions
Class	5491c	Isogeny class
Conductor	5491	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	28288	Modular degree for the optimal curve
Δ	42810223415417 = 179 · 192	Discriminant
Eigenvalues	1  2 -4 -2 -6 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-38587,2884440]	[a1,a2,a3,a4,a6]
j	53582633/361	j-invariant
L	0.64555651677789	L(r)(E,1)/r!
Ω	0.64555651677789	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	87856m1 49419i1 5491d1 104329f1	Quadratic twists by: -4 -3 17 -19

Hecke Eigenvalues for elliptic curve 5491c1

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 5491c1

-4	-3	17	-19
87856m1	49419i1	5491d1	104329f1

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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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