Cremona's table of elliptic curves

5681 = 13 · 19 · 23

Field	Data	Notes
Atkin-Lehner	13+ 19+ 23+	Signs for the Atkin-Lehner involutions
Class	5681a	Isogeny class
Conductor	5681	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	568	Modular degree for the optimal curve
Δ	-130663 = -1 · 13 · 19 · 232	Discriminant
Eigenvalues	1 -2 -4  0  0 13+ -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3,17]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	-1771561/130663	j-invariant
L	1.9267995583903	L(r)(E,1)/r!
Ω	2.7136682702596	Real period
R	1.420070079683	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	90896p1 51129g1 73853d1 107939h1	Quadratic twists by: -4 -3 13 -19

Hecke Eigenvalues for elliptic curve 5681a1

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	0	0	+	-2	+	+	6	0	-2	-2	4	6	12	-12	6	-4	8	-2	8	-4	-2	-2

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Quadratic twists for elliptic curve 5681a1

-4	-3	13	-19
90896p1	51129g1	73853d1	107939h1

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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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