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	17808b	Isogeny class
Conductor	17808	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-97730304 = -1 · 28 · 3 · 74 · 53	Discriminant
Eigenvalues	2+ 3+  2 7+  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12,480]	[a1,a2,a3,a4,a6]
Generators	[17:70:1]	Generators of the group modulo torsion
j	-810448/381759	j-invariant
L	4.7636355038071	L(r)(E,1)/r!
Ω	1.5368274319672	Real period
R	3.0996554360756	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	8904c1 71232db1 53424g1 124656bc1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17808b1

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	-2	-2	-4	0	-6	4	-10	6	4	8	+	0	6	8	8	6	16	-12	6	-14

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Quadratic twists for elliptic curve 17808b1

-4	8	-3	-7
8904c1	71232db1	53424g1	124656bc1

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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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