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	5850bc	Isogeny class
Conductor	5850	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	-6855468750 = -1 · 2 · 33 · 510 · 13	Discriminant
Eigenvalues	2- 3+ 5+ -2 -6 13+  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-27305,1743447]	[a1,a2,a3,a4,a6]
j	-8538302475/26	j-invariant
L	2.3182592310578	L(r)(E,1)/r!
Ω	1.1591296155289	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	46800bz1 5850a2 5850g1 76050g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850bc1

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 5850bc1

-4	-3	5	13
46800bz1	5850a2	5850g1	76050g1

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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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