Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 29+	Signs for the Atkin-Lehner involutions
Class	1682a	Isogeny class
Conductor	1682	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-17663873340416 = -1 · 210 · 297	Discriminant
Eigenvalues	2+  1  1 -2  3 -1 -8  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,4187,173584]	[a1,a2,a3,a4,a6]
Generators	[563:13174:1]	Generators of the group modulo torsion
j	13651919/29696	j-invariant
L	2.5019223359355	L(r)(E,1)/r!
Ω	0.47965454464656	Real period
R	1.3040230536016	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13456f1 53824d1 15138v1 42050u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682a1

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	3	-1	-8	0	4	+	3	-8	-2	11	-13	-11	0	8	-12	2	-4	-15	4	10	2

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Quadratic twists for elliptic curve 1682a1

-4	8	-3	5	-7	29
13456f1	53824d1	15138v1	42050u1	82418a1	58b1

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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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