Cremona's table of elliptic curves

1328 = 2⁴ · 83

Field	Data	Notes
Atkin-Lehner	2- 83-	Signs for the Atkin-Lehner involutions
Class	1328d	Isogeny class
Conductor	1328	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-5439488 = -1 · 216 · 83	Discriminant
Eigenvalues	2-  1 -2 -1  5 -2 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-104,-460]	[a1,a2,a3,a4,a6]
Generators	[14:32:1]	Generators of the group modulo torsion
j	-30664297/1328	j-invariant
L	2.7715864413396	L(r)(E,1)/r!
Ω	0.74501499070518	Real period
R	0.93004385009629	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	166a1 5312h1 11952n1 33200v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1328d1

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	-2	-1	5	-2	-3	2	-4	-3	-1	1	6	-8	-12	-14	3	-7	-2	14	-4	6	-	4	12

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Quadratic twists for elliptic curve 1328d1

-4	8	-3	5	-7	-83
166a1	5312h1	11952n1	33200v1	65072t1	110224j1

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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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