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	1785o	Isogeny class
Conductor	1785	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	14387797265625 = 32 · 58 · 72 · 174	Discriminant
Eigenvalues	-1 3- 5- 7- -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6115,-24400]	[a1,a2,a3,a4,a6]
Generators	[-55:410:1]	Generators of the group modulo torsion
j	25288177725059761/14387797265625	j-invariant
L	2.3616383858566	L(r)(E,1)/r!
Ω	0.58350917126968	Real period
R	0.50591286781274	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	28560cv4 114240bh4 5355f3 8925b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785o3

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	-8	6	0	-10	-6	-4	0	6	-4	6	4	8	2	-16	-12	-6	10

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Quadratic twists for elliptic curve 1785o3

-4	8	-3	5	-7	17
28560cv4	114240bh4	5355f3	8925b3	12495b3	30345c4

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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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