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
Δ	-48802039062823316 = -1 · 22 · 2911	Discriminant
Eigenvalues	2+  1  1 -2  3 -1 -8  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-382673,-91764536]	[a1,a2,a3,a4,a6]
Generators	[94445:841652:125]	Generators of the group modulo torsion
j	-10418796526321/82044596	j-invariant
L	2.5019223359355	L(r)(E,1)/r!
Ω	0.095930908929312	Real period
R	6.5201152680079	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	13456f2 53824d2 15138v2 42050u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682a2

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 1682a2

-4	8	-3	5	-7	29
13456f2	53824d2	15138v2	42050u2	82418a2	58b2

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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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