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	5850r	Isogeny class
Conductor	5850	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	115500937500000 = 25 · 37 · 510 · 132	Discriminant
Eigenvalues	2+ 3- 5+ -4  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-19468917,-33059545259]	[a1,a2,a3,a4,a6]
Generators	[5109:25883:1]	Generators of the group modulo torsion
j	71647584155243142409/10140000	j-invariant
L	2.5540254677524	L(r)(E,1)/r!
Ω	0.071872724025515	Real period
R	4.4419240789553	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	46800eh4 1950q4 1170n3 76050ew4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850r3

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	0	-	-2	4	8	-2	-8	-2	6	-12	0	10	0	-10	4	16	6	-8	-4	14	6

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Quadratic twists for elliptic curve 5850r3

-4	-3	5	13
46800eh4	1950q4	1170n3	76050ew4

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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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