Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 29-	Signs for the Atkin-Lehner involutions
Class	1682d	Isogeny class
Conductor	1682	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2900	Modular degree for the optimal curve
Δ	1000492825922 = 2 · 298	Discriminant
Eigenvalues	2+ -2  0 -1 -6 -4 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2541,10430]	[a1,a2,a3,a4,a6]
j	3625/2	j-invariant
L	0.25416768499355	L(r)(E,1)/r!
Ω	0.76250305498065	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13456o1 53824o1 15138z1 42050bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682d1

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 1682d1

-4	8	-3	5	-7	29
13456o1	53824o1	15138z1	42050bd1	82418i1	1682f1

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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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