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	5850q	Isogeny class
Conductor	5850	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-13327031250000 = -1 · 24 · 38 · 510 · 13	Discriminant
Eigenvalues	2+ 3- 5+  3  3 13- -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2051156367,35756293724541]	[a1,a2,a3,a4,a6]
Generators	[8968974:-4451313:343]	Generators of the group modulo torsion
j	-134057911417971280740025/1872	j-invariant
L	3.3651969669352	L(r)(E,1)/r!
Ω	0.16323199217897	Real period
R	5.1540095204586	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	46800eg2 1950y2 5850bw1 76050ev2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850q2

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
+	-	+	3	3	-	-3	0	-4	-5	-3	-12	-2	4	-3	-9	-15	-3	-7	8	-16	0	1	0	-2

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Quadratic twists for elliptic curve 5850q2

-4	-3	5	13
46800eg2	1950y2	5850bw1	76050ev2

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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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