Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	1682i	Isogeny class
Conductor	1682	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-25573720064 = -1 · 220 · 293	Discriminant
Eigenvalues	2-  1 -1 -2 -5  1 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,374,7204]	[a1,a2,a3,a4,a6]
Generators	[12:110:1]	Generators of the group modulo torsion
j	237176659/1048576	j-invariant
L	4.1385484798886	L(r)(E,1)/r!
Ω	0.85329516434063	Real period
R	0.12125196101066	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	13456n2 53824n2 15138l2 42050l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682i2

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 1682i2

-4	8	-3	5	-7	29
13456n2	53824n2	15138l2	42050l2	82418v2	1682c2

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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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