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	128	Product of Tamagawa factors cp
Δ	74955488400000000 = 210 · 38 · 58 · 134	Discriminant
Eigenvalues	2+ 3- 5+ -4  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1216917,-516229259]	[a1,a2,a3,a4,a6]
Generators	[-637:728:1]	Generators of the group modulo torsion
j	17496824387403529/6580454400	j-invariant
L	2.5540254677524	L(r)(E,1)/r!
Ω	0.14374544805103	Real period
R	2.2209620394777	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	46800eh2 1950q2 1170n2 76050ew2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850r2

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 5850r2

-4	-3	5	13
46800eh2	1950q2	1170n2	76050ew2

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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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