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	850c	Isogeny class
Conductor	850	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	-4250000000 = -1 · 27 · 59 · 17	Discriminant
Eigenvalues	2+  1 5-  0 -6  3 17- -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-451,4798]	[a1,a2,a3,a4,a6]
Generators	[2:61:1]	Generators of the group modulo torsion
j	-5177717/2176	j-invariant
L	1.9776460914019	L(r)(E,1)/r!
Ω	1.2971425666887	Real period
R	0.7623086861032	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	6800x1 27200bk1 7650cg1 850l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850c1

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 850c1

-4	8	-3	5	-7	-11	17
6800x1	27200bk1	7650cg1	850l1	41650y1	102850cx1	14450j1

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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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