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	1785c	Isogeny class
Conductor	1785	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6452105625 = 36 · 54 · 72 · 172	Discriminant
Eigenvalues	-1 3+ 5+ 7-  0 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3826,-92602]	[a1,a2,a3,a4,a6]
j	6193921595708449/6452105625	j-invariant
L	0.60707155472399	L(r)(E,1)/r!
Ω	0.60707155472399	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28560de2 114240em2 5355p2 8925t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785c2

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	-2	+	0	4	-6	0	-2	6	-12	8	6	-12	2	-4	-12	-2	0	12	14	14

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Quadratic twists for elliptic curve 1785c2

-4	8	-3	5	-7	17
28560de2	114240em2	5355p2	8925t2	12495q2	30345bf2

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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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