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	1683c	Isogeny class
Conductor	1683	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	250687795157217 = 33 · 113 · 178	Discriminant
Eigenvalues	1 3+ -4 -2 11- -2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-83604,-9252301]	[a1,a2,a3,a4,a6]
j	2393558463315519963/9284733153971	j-invariant
L	0.84249072782713	L(r)(E,1)/r!
Ω	0.28083024260904	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	26928w1 107712d1 1683b1 42075m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683c1

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

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Quadratic twists for elliptic curve 1683c1

-4	8	-3	5	-7	-11	17
26928w1	107712d1	1683b1	42075m1	82467f1	18513e1	28611a1

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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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