Cremona's table of elliptic curves

5687 = 11² · 47

Field	Data	Notes
Atkin-Lehner	11- 47-	Signs for the Atkin-Lehner involutions
Class	5687b	Isogeny class
Conductor	5687	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-5208706449419 = -1 · 119 · 472	Discriminant
Eigenvalues	-2 -1  3 -4 11-  0  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,4316,-13652]	[a1,a2,a3,a4,a6]
Generators	[59:665:1]	Generators of the group modulo torsion
j	5017776128/2940179	j-invariant
L	1.6179883963187	L(r)(E,1)/r!
Ω	0.45038459668586	Real period
R	0.44905743008991	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	90992k1 51183e1 517a1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 5687b1

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
-2	-1	3	-4	-	0	0	-2	1	-2	-3	3	2	12	-	-10	9	10	-5	9	4	10	-4	-13	-15

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Quadratic twists for elliptic curve 5687b1

-4	-3	-11
90992k1	51183e1	517a1

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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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