Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 29-	Signs for the Atkin-Lehner involutions
Conductor	1682	Conductor
Count	2	Number of curves in isogeny class
Curves	1682c1 1682c2	Curves in isogeny class
deg	6496	Modular degree for the optimal curve
Eigenvalues	2+ -1 -1 -2  5  1  2 -4	Hecke eigenvalues for primes less than 20
L	0.63381173642831	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	13456m 53824m 15138bc 42050bc	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 1682c

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 isogeny class 1682c

-4	8	-3	5	-7	29
13456m	53824m	15138bc	42050bc	82418e	1682i

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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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