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	17850cg	Isogeny class
Conductor	17850	Conductor
∏ cp	1440	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	-36533824782336000 = -1 · 220 · 39 · 53 · 72 · 172	Discriminant
Eigenvalues	2- 3- 5- 7+ -2 -4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,71452,-5519088]	[a1,a2,a3,a4,a6]
Generators	[712:-20516:1]	Generators of the group modulo torsion
j	322742744589591019/292270598258688	j-invariant
L	8.641592007154	L(r)(E,1)/r!
Ω	0.20072068984532	Real period
R	0.11959117049963	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	53550ce1 17850m1 124950gm1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17850cg1

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

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Quadratic twists for elliptic curve 17850cg1

-3	5	-7
53550ce1	17850m1	124950gm1

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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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