Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	1682h	Isogeny class
Conductor	1682	Conductor
∏ cp	11	Product of Tamagawa factors cp
deg	47850	Modular degree for the optimal curve
Δ	-861608413798811648 = -1 · 211 · 2910	Discriminant
Eigenvalues	2- -3  0  4  1  6 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,221025,19814919]	[a1,a2,a3,a4,a6]
j	2838375/2048	j-invariant
L	1.9662954914802	L(r)(E,1)/r!
Ω	0.17875413558911	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	13456j1 53824i1 15138f1 42050i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682h1

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	0	4	1	6	-2	-1	-6	+	0	8	11	-1	4	-2	-4	8	8	-2	-6	4	15	-3	3

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Quadratic twists for elliptic curve 1682h1

-4	8	-3	5	-7	29
13456j1	53824i1	15138f1	42050i1	82418r1	1682e1

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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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