Cremona's table of elliptic curves

323 = 17 · 19

Field	Data	Notes
Atkin-Lehner	17+ 19-	Signs for the Atkin-Lehner involutions
Class	323a	Isogeny class
Conductor	323	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	140	Modular degree for the optimal curve
Δ	-26977283 = -1 · 175 · 19	Discriminant
Eigenvalues	0  3 -2  4 -2  6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-46,277]	[a1,a2,a3,a4,a6]
j	-10764582912/26977283	j-invariant
L	1.8660949119674	L(r)(E,1)/r!
Ω	1.8660949119674	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5168e1 20672f1 2907b1 8075f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 323a1

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
0	3	-2	4	-2	6	+	-	0	-9	-9	2	-6	-1	-3	2	14	-6	-14	16	-2	8	-3	2	-7

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Quadratic twists for elliptic curve 323a1

-4	8	-3	5	-7	-11	13	17	-19
5168e1	20672f1	2907b1	8075f1	15827j1	39083f1	54587a1	5491b1	6137a1

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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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