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	17850cd	Isogeny class
Conductor	17850	Conductor
∏ cp	480	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	-27856710000000000 = -1 · 210 · 34 · 510 · 7 · 173	Discriminant
Eigenvalues	2- 3- 5+ 7-  2 -4 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-42088,-8694208]	[a1,a2,a3,a4,a6]
Generators	[512:9944:1]	Generators of the group modulo torsion
j	-527690404915129/1782829440000	j-invariant
L	9.3514555797748	L(r)(E,1)/r!
Ω	0.15325484529296	Real period
R	0.5084915674226	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53550bo1 3570a1 124950fa1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17850cd1

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	-4	-8	-8	4	10	4	-4	-10	10	6	0	-12	-6	-8	-14	-10	-2

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Quadratic twists for elliptic curve 17850cd1

-3	5	-7
53550bo1	3570a1	124950fa1

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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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