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	850f	Isogeny class
Conductor	850	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-164135469200 = -1 · 24 · 52 · 177	Discriminant
Eigenvalues	2- -1 5+  5  4 -3 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1357,-2559]	[a1,a2,a3,a4,a6]
j	11053587253415/6565418768	j-invariant
L	2.3875691311524	L(r)(E,1)/r!
Ω	0.5968922827881	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	6800j1 27200e1 7650ba1 850d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850f1

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	+	5	4	-3	+	-2	8	0	-5	12	-10	4	2	1	0	2	-8	5	-4	-17	16	-6	-16

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Quadratic twists for elliptic curve 850f1

-4	8	-3	5	-7	-11	17
6800j1	27200e1	7650ba1	850d1	41650cb1	102850t1	14450u1

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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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