Cremona's table of elliptic curves

850 = 2 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 5- 17+	Signs for the Atkin-Lehner involutions
Class	850l	Isogeny class
Conductor	850	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-272000 = -1 · 27 · 53 · 17	Discriminant
Eigenvalues	2- -1 5-  0 -6 -3 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18,31]	[a1,a2,a3,a4,a6]
Generators	[5:-13:1]	Generators of the group modulo torsion
j	-5177717/2176	j-invariant
L	2.7415419874287	L(r)(E,1)/r!
Ω	2.9004989556244	Real period
R	0.067514048675573	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	6800u1 27200bc1 7650bf1 850c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850l1

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	-	0	-6	-3	+	-7	8	-5	5	-8	0	4	-3	-9	5	-3	2	-15	11	8	-4	-1	9

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Quadratic twists for elliptic curve 850l1

-4	8	-3	5	-7	-11	17
6800u1	27200bc1	7650bf1	850c1	41650co1	102850bs1	14450bf1

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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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