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	28676025 = 34 · 52 · 72 · 172	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-111,360]	[a1,a2,a3,a4,a6]
Generators	[-9:30:1]	Generators of the group modulo torsion
j	151334226289/28676025	j-invariant
L	2.1569213922132	L(r)(E,1)/r!
Ω	1.9943115779429	Real period
R	0.54076840752188	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28560cf2 114240cd2 5355q2 8925d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785k2

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 1785k2

-4	8	-3	5	-7	17
28560cf2	114240cd2	5355q2	8925d2	12495h2	30345m2

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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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