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	850j	Isogeny class
Conductor	850	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-2656250 = -1 · 2 · 57 · 17	Discriminant
Eigenvalues	2- -3 5+ -2 -4  3 17+  3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-255,-1503]	[a1,a2,a3,a4,a6]
j	-116930169/170	j-invariant
L	1.1949776914903	L(r)(E,1)/r!
Ω	0.59748884574513	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	6800o1 27200p1 7650w1 170e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850j1

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
-	-3	+	-2	-4	3	+	3	6	9	-3	8	-6	-6	13	9	15	7	2	9	3	0	-12	-9	-7

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Quadratic twists for elliptic curve 850j1

-4	8	-3	5	-7	-11	17
6800o1	27200p1	7650w1	170e1	41650cg1	102850bc1	14450z1

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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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