Cremona's table of elliptic curves

1682 = 2 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 29+	Signs for the Atkin-Lehner involutions
Class	1682b	Isogeny class
Conductor	1682	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	300	Modular degree for the optimal curve
Δ	26912 = 25 · 292	Discriminant
Eigenvalues	2+ -2 -2 -5  0  2  7  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-47,-126]	[a1,a2,a3,a4,a6]
Generators	[-4:2:1]	Generators of the group modulo torsion
j	13239457/32	j-invariant
L	1.1365355772867	L(r)(E,1)/r!
Ω	1.8283139026291	Real period
R	0.62163044084077	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	13456h1 53824g1 15138x1 42050v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1682b1

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	-2	-5	0	2	7	6	1	+	3	-2	-2	-10	-7	-2	-12	8	-6	11	-7	-3	4	13	11

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Quadratic twists for elliptic curve 1682b1

-4	8	-3	5	-7	29
13456h1	53824g1	15138x1	42050v1	82418d1	1682j1

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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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