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	10850v	Isogeny class
Conductor	10850	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-911779750000000000 = -1 · 210 · 512 · 76 · 31	Discriminant
Eigenvalues	2-  2 5+ 7+  0 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,160812,38725781]	[a1,a2,a3,a4,a6]
Generators	[1425:55537:1]	Generators of the group modulo torsion
j	29434650064089479/58353904000000	j-invariant
L	8.9141789150752	L(r)(E,1)/r!
Ω	0.1932199864238	Real period
R	2.3067434896521	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	86800bx1 97650y1 2170h1 75950ci1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10850v1

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

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Quadratic twists for elliptic curve 10850v1

-4	-3	5	-7
86800bx1	97650y1	2170h1	75950ci1

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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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