Cremona's table of elliptic curves

1683 = 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	3+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	1683a	Isogeny class
Conductor	1683	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	10385793 = 33 · 113 · 172	Discriminant
Eigenvalues	1 3+  2 -2 11+ -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-66,-121]	[a1,a2,a3,a4,a6]
Generators	[10:7:1]	Generators of the group modulo torsion
j	1187648379/384659	j-invariant
L	3.5972318929792	L(r)(E,1)/r!
Ω	1.7168933367098	Real period
R	2.0951982374589	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26928ba1 107712m1 1683d1 42075f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683a1

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	+	2	-2	+	-2	+	8	-4	-6	-8	-2	-6	-8	-6	0	6	-4	4	4	0	-6	16	-4	2

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Quadratic twists for elliptic curve 1683a1

-4	8	-3	5	-7	-11	17
26928ba1	107712m1	1683d1	42075f1	82467c1	18513d1	28611d1

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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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