Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 29-	Signs for the Atkin-Lehner involutions
Class	1682c	Isogeny class
Conductor	1682	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6496	Modular degree for the optimal curve
Δ	-232114335613904 = -1 · 24 · 299	Discriminant
Eigenvalues	2+ -1 -1 -2  5  1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-51318,-4555676]	[a1,a2,a3,a4,a6]
j	-1030301/16	j-invariant
L	0.63381173642831	L(r)(E,1)/r!
Ω	0.15845293410708	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13456m1 53824m1 15138bc1 42050bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682c1

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	-1	-2	5	1	2	-4	-6	-	-5	8	-10	9	3	-1	10	10	-8	8	16	1	14	-14	-2

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Quadratic twists for elliptic curve 1682c1

-4	8	-3	5	-7	29
13456m1	53824m1	15138bc1	42050bc1	82418e1	1682i1

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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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