Cremona's table of elliptic curves

18785 = 5 · 13 · 17²

Field	Data	Notes
Atkin-Lehner	5- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	18785c	Isogeny class
Conductor	18785	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	1568941985 = 5 · 13 · 176	Discriminant
Eigenvalues	-1  2 5-  4 -2 13+ 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-295,292]	[a1,a2,a3,a4,a6]
j	117649/65	j-invariant
L	2.6110674619283	L(r)(E,1)/r!
Ω	1.3055337309641	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	93925i1 65a1	Quadratic twists by: 5 17

Hecke Eigenvalues for elliptic curve 18785c1

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
-1	2	-	4	-2	+	+	-6	6	-2	10	2	6	10	4	2	6	-2	-4	-6	6	12	-16	2	2

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Quadratic twists for elliptic curve 18785c1

5	17
93925i1	65a1

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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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