Cremona's table of elliptic curves

5814 = 2 · 3² · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 17- 19-	Signs for the Atkin-Lehner involutions
Class	5814u	Isogeny class
Conductor	5814	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	286327872 = 26 · 36 · 17 · 192	Discriminant
Eigenvalues	2- 3- -4 -2 -4  6 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1127,14815]	[a1,a2,a3,a4,a6]
Generators	[17:10:1]	Generators of the group modulo torsion
j	216973458729/392768	j-invariant
L	4.324219764176	L(r)(E,1)/r!
Ω	1.7340878188585	Real period
R	0.41560945541025	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	46512bg1 646a1 98838bo1 110466y1	Quadratic twists by: -4 -3 17 -19

Hecke Eigenvalues for elliptic curve 5814u1

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
-	-	-4	-2	-4	6	-	-	6	0	6	-4	-6	-4	0	-14	4	0	4	-10	10	-10	12	-14	-10

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Quadratic twists for elliptic curve 5814u1

-4	-3	17	-19
46512bg1	646a1	98838bo1	110466y1

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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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