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	1785l	Isogeny class
Conductor	1785	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-6559875 = -1 · 32 · 53 · 73 · 17	Discriminant
Eigenvalues	0 3- 5+ 7- -6 -1 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-12381,-534400]	[a1,a2,a3,a4,a6]
j	-209906535145406464/6559875	j-invariant
L	1.3577785848007	L(r)(E,1)/r!
Ω	0.22629643080011	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28560cm2 114240cp2 5355o2 8925a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785l2

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
0	-	+	-	-6	-1	-	2	3	0	5	5	9	8	-9	0	0	5	8	6	-16	2	3	6	2

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Quadratic twists for elliptic curve 1785l2

-4	8	-3	5	-7	17
28560cm2	114240cp2	5355o2	8925a2	12495d2	30345i2

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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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