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	2	Product of Tamagawa factors cp
Δ	316207395 = 312 · 5 · 7 · 17	Discriminant
Eigenvalues	1 3+ 5+ 7- -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3188,-70623]	[a1,a2,a3,a4,a6]
j	3585019225176649/316207395	j-invariant
L	1.2706751423104	L(r)(E,1)/r!
Ω	0.6353375711552	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	28560dg4 114240er4 5355s4 8925u3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785b3

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 1785b3

-4	8	-3	5	-7	17
28560dg4	114240er4	5355s4	8925u3	12495p4	30345be4

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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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