Cremona's table of elliptic curves

17850 = 2 · 3 · 5² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	17850bo	Isogeny class
Conductor	17850	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3712	Modular degree for the optimal curve
Δ	-1249500 = -1 · 22 · 3 · 53 · 72 · 17	Discriminant
Eigenvalues	2- 3+ 5- 7- -4  4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18,-69]	[a1,a2,a3,a4,a6]
j	-5177717/9996	j-invariant
L	2.1801329413887	L(r)(E,1)/r!
Ω	1.0900664706944	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	53550cm1 17850x1 124950jg1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17850bo1

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
-	+	-	-	-4	4	+	-4	-8	2	-8	-6	-10	2	0	10	10	6	2	0	10	2	12	12	-2

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Quadratic twists for elliptic curve 17850bo1

-3	5	-7
53550cm1	17850x1	124950jg1

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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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