Cremona's table of elliptic curves

10850 = 2 · 5² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 31+	Signs for the Atkin-Lehner involutions
Class	10850d	Isogeny class
Conductor	10850	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-59335937500 = -1 · 22 · 510 · 72 · 31	Discriminant
Eigenvalues	2+ -2 5+ 7+  6  0  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,374,-11352]	[a1,a2,a3,a4,a6]
Generators	[22:76:1]	Generators of the group modulo torsion
j	371694959/3797500	j-invariant
L	2.4110505566733	L(r)(E,1)/r!
Ω	0.54808441716972	Real period
R	1.0997624093766	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	86800cd1 97650de1 2170p1 75950bf1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10850d1

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	6	0	-4	0	+	4	-10	-6	0	-4	4	-8	-4	-8	10	4	-6	-6	-6

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Quadratic twists for elliptic curve 10850d1

-4	-3	5	-7
86800cd1	97650de1	2170p1	75950bf1

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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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