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	5850g	Isogeny class
Conductor	5850	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	-438750 = -1 · 2 · 33 · 54 · 13	Discriminant
Eigenvalues	2+ 3+ 5-  2 -6 13-  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1092,14166]	[a1,a2,a3,a4,a6]
Generators	[15:24:1]	Generators of the group modulo torsion
j	-8538302475/26	j-invariant
L	2.9436323040211	L(r)(E,1)/r!
Ω	2.5918926150558	Real period
R	1.7035614941696	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	46800cr1 5850bi2 5850bc1 76050dx1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850g1

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	-6	-	0	-1	-6	3	8	-1	9	8	3	-3	6	-10	-13	-9	-4	11	-12	6	-10

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Quadratic twists for elliptic curve 5850g1

-4	-3	5	13
46800cr1	5850bi2	5850bc1	76050dx1

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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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