Cremona's table of elliptic curves

5850 = 2 · 3² · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 13-	Signs for the Atkin-Lehner involutions
Class	5850ba	Isogeny class
Conductor	5850	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	12933148176000 = 27 · 314 · 53 · 132	Discriminant
Eigenvalues	2+ 3- 5- -4  6 13-  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-31707,-2158299]	[a1,a2,a3,a4,a6]
j	38686490446661/141927552	j-invariant
L	1.4314162239634	L(r)(E,1)/r!
Ω	0.35785405599086	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	46800fo2 1950bb2 5850by2 76050gd2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850ba2

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	6	-	4	2	6	10	4	-6	-10	0	-8	6	6	-6	-12	0	2	-8	4	-14	14

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Quadratic twists for elliptic curve 5850ba2

-4	-3	5	13
46800fo2	1950bb2	5850by2	76050gd2

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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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