Cremona's table of elliptic curves

1343 = 17 · 79

Field	Data	Notes
Atkin-Lehner	17- 79-	Signs for the Atkin-Lehner involutions
Class	1343a	Isogeny class
Conductor	1343	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	176	Modular degree for the optimal curve
Δ	6598159 = 174 · 79	Discriminant
Eigenvalues	-1  1  1  1 -2 -5 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-50,53]	[a1,a2,a3,a4,a6]
Generators	[-7:12:1]	Generators of the group modulo torsion
j	13841287201/6598159	j-invariant
L	2.1357059909233	L(r)(E,1)/r!
Ω	2.1154154719403	Real period
R	0.2523979354472	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	21488h1 85952k1 12087i1 33575d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1343a1

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	1	1	-2	-5	-	8	-6	-2	-2	-6	6	-4	-3	8	-1	12	-12	-7	10	-	-10	-7	-7

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Quadratic twists for elliptic curve 1343a1

-4	8	-3	5	-7	17	-79
21488h1	85952k1	12087i1	33575d1	65807a1	22831a1	106097b1

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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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