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	5850br	Isogeny class
Conductor	5850	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-399810937500 = -1 · 22 · 39 · 58 · 13	Discriminant
Eigenvalues	2- 3- 5+ -2 -4 13-  8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,895,28397]	[a1,a2,a3,a4,a6]
j	6967871/35100	j-invariant
L	2.7272258551456	L(r)(E,1)/r!
Ω	0.68180646378639	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	46800dz1 1950i1 1170e1 76050bl1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850br1

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

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Quadratic twists for elliptic curve 5850br1

-4	-3	5	13
46800dz1	1950i1	1170e1	76050bl1

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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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