Cremona's table of elliptic curves

17808 = 2⁴ · 3 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 53-	Signs for the Atkin-Lehner involutions
Class	17808k	Isogeny class
Conductor	17808	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	77824	Modular degree for the optimal curve
Δ	-228950700926976 = -1 · 211 · 316 · 72 · 53	Discriminant
Eigenvalues	2+ 3- -3 7+ -3 -4  5 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,15248,-64204]	[a1,a2,a3,a4,a6]
Generators	[38:756:1]	Generators of the group modulo torsion
j	191427323574814/111792334437	j-invariant
L	4.0822325283094	L(r)(E,1)/r!
Ω	0.32929442097968	Real period
R	0.096850841057477	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	8904f1 71232ca1 53424b1 124656p1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17808k1

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
+	-	-3	+	-3	-4	5	-8	3	8	-1	0	2	3	0	-	9	10	12	12	6	-1	-16	-5	1

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Quadratic twists for elliptic curve 17808k1

-4	8	-3	-7
8904f1	71232ca1	53424b1	124656p1

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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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