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	10850u	Isogeny class
Conductor	10850	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	159661140625000 = 23 · 59 · 73 · 313	Discriminant
Eigenvalues	2- -1 5+ 7+  3 -5  6 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-16338,519031]	[a1,a2,a3,a4,a6]
Generators	[-5:777:1]	Generators of the group modulo torsion
j	30867540216409/10218313000	j-invariant
L	5.3524801572618	L(r)(E,1)/r!
Ω	0.53040401225278	Real period
R	0.56062925971053	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	86800bt2 97650bf2 2170c2 75950cf2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10850u2

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
-	-1	+	+	3	-5	6	-7	9	-6	-	-2	0	-8	3	0	9	8	4	-15	16	-10	-15	-15	1

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Quadratic twists for elliptic curve 10850u2

-4	-3	5	-7
86800bt2	97650bf2	2170c2	75950cf2

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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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