Cremona's table of elliptic curves

1785 = 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	1785k	Isogeny class
Conductor	1785	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1339001685 = 38 · 5 · 74 · 17	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-536,-4485]	[a1,a2,a3,a4,a6]
Generators	[-11:16:1]	Generators of the group modulo torsion
j	17032120495489/1339001685	j-invariant
L	2.1569213922132	L(r)(E,1)/r!
Ω	0.99715578897143	Real period
R	0.27038420376094	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	28560cf3 114240cd3 5355q4 8925d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785k3

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	-	+	-	0	-6	+	4	0	-2	0	-6	-10	4	4	6	4	-14	-12	12	-10	-12	16	-6	-18

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Quadratic twists for elliptic curve 1785k3

-4	8	-3	5	-7	17
28560cf3	114240cd3	5355q4	8925d3	12495h4	30345m3

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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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