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	850i	Isogeny class
Conductor	850	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-2656250000 = -1 · 24 · 510 · 17	Discriminant
Eigenvalues	2-  3 5+  1 -4 -3 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,195,2197]	[a1,a2,a3,a4,a6]
j	84375/272	j-invariant
L	4.0702155151156	L(r)(E,1)/r!
Ω	1.0175538787789	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	6800p1 27200q1 7650t1 850e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850i1

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	+	1	-4	-3	+	6	0	0	-9	-4	6	-12	10	9	0	-14	8	-15	12	3	0	-6	-16

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Quadratic twists for elliptic curve 850i1

-4	8	-3	5	-7	-11	17
6800p1	27200q1	7650t1	850e1	41650ch1	102850bb1	14450bb1

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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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