Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	1682g	Isogeny class
Conductor	1682	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-68999505236 = -1 · 22 · 297	Discriminant
Eigenvalues	2-  3 -3 -2  1  3  4  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-999,17779]	[a1,a2,a3,a4,a6]
j	-185193/116	j-invariant
L	4.0597395954496	L(r)(E,1)/r!
Ω	1.0149348988624	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	13456l1 53824j1 15138h1 42050j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682g1

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
-	3	-3	-2	1	3	4	8	0	+	-3	8	2	-7	-11	1	-4	-4	-4	-2	12	7	0	6	6

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Quadratic twists for elliptic curve 1682g1

-4	8	-3	5	-7	29
13456l1	53824j1	15138h1	42050j1	82418s1	58a1

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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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