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	5850bm	Isogeny class
Conductor	5850	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	2635153889062500 = 22 · 310 · 58 · 134	Discriminant
Eigenvalues	2- 3- 5+  0 -4 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-127130,17302997]	[a1,a2,a3,a4,a6]
Generators	[229:285:1]	Generators of the group modulo torsion
j	19948814692561/231344100	j-invariant
L	5.6593423796039	L(r)(E,1)/r!
Ω	0.45728912776914	Real period
R	3.0939628978349	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	46800cx3 1950g3 1170d4 76050bc3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850bm4

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
-	-	+	0	-4	+	-6	4	8	-6	-8	10	6	-4	0	-10	-4	-2	12	-16	-2	-16	-12	-10	6

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Quadratic twists for elliptic curve 5850bm4

-4	-3	5	13
46800cx3	1950g3	1170d4	76050bc3

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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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