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	5850bg	Isogeny class
Conductor	5850	Conductor
∏ cp	640	Product of Tamagawa factors cp
deg	122880	Modular degree for the optimal curve
Δ	-6415943040000000000 = -1 · 216 · 33 · 510 · 135	Discriminant
Eigenvalues	2- 3+ 5+ -2 -4 13- -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,420145,62058647]	[a1,a2,a3,a4,a6]
Generators	[339:15430:1]	Generators of the group modulo torsion
j	19441890357117957/15208161280000	j-invariant
L	5.4381023824278	L(r)(E,1)/r!
Ω	0.15282155740255	Real period
R	0.22240409316497	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	46800ci1 5850e1 1170a1 76050f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850bg1

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

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Quadratic twists for elliptic curve 5850bg1

-4	-3	5	13
46800ci1	5850e1	1170a1	76050f1

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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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