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	850b	Isogeny class
Conductor	850	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	754299031250 = 2 · 56 · 176	Discriminant
Eigenvalues	2+  2 5+  4  6 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2825,-41125]	[a1,a2,a3,a4,a6]
j	159661140625/48275138	j-invariant
L	2.0105217603181	L(r)(E,1)/r!
Ω	0.67017392010602	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6800t4 27200z4 7650by4 34a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850b4

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
+	2	+	4	6	-2	-	-4	0	0	-4	4	6	-8	0	6	0	-4	-8	0	-2	8	0	-6	-14

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Quadratic twists for elliptic curve 850b4

-4	8	-3	5	-7	-11	17
6800t4	27200z4	7650by4	34a4	41650n4	102850ce4	14450g4

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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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