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	1785b	Isogeny class
Conductor	1785	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	9865918125 = 33 · 54 · 7 · 174	Discriminant
Eigenvalues	1 3+ 5+ 7- -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1158,13923]	[a1,a2,a3,a4,a6]
j	171963096231529/9865918125	j-invariant
L	1.2706751423104	L(r)(E,1)/r!
Ω	1.2706751423104	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28560dg3 114240er3 5355s3 8925u4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785b4

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

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Quadratic twists for elliptic curve 1785b4

-4	8	-3	5	-7	17
28560dg3	114240er3	5355s3	8925u4	12495p3	30345be3

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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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