Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	1682f	Isogeny class
Conductor	1682	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	100	Modular degree for the optimal curve
Δ	1682 = 2 · 292	Discriminant
Eigenvalues	2-  2  0 -1  6 -4  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3,-1]	[a1,a2,a3,a4,a6]
j	3625/2	j-invariant
L	4.1062046170143	L(r)(E,1)/r!
Ω	4.1062046170143	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	13456i1 53824h1 15138d1 42050g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682f1

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
-	2	0	-1	6	-4	3	4	9	+	-5	-2	6	4	9	-12	6	-2	8	3	-11	-11	0	-3	-17

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Quadratic twists for elliptic curve 1682f1

-4	8	-3	5	-7	29
13456i1	53824h1	15138d1	42050g1	82418q1	1682d1

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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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