Cremona's table of elliptic curves

3519 = 3² · 17 · 23

Field	Data	Notes
Atkin-Lehner	3+ 17+ 23+	Signs for the Atkin-Lehner involutions
Class	3519a	Isogeny class
Conductor	3519	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	7696053 = 39 · 17 · 23	Discriminant
Eigenvalues	0 3+  2 -3  0  3 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-54,74]	[a1,a2,a3,a4,a6]
Generators	[-6:13:1]	Generators of the group modulo torsion
j	884736/391	j-invariant
L	3.0668389654075	L(r)(E,1)/r!
Ω	2.1071676895083	Real period
R	0.72771592424214	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	56304s1 3519b1 87975j1 59823b1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3519a1

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	+	2	-3	0	3	+	0	+	-7	4	-5	-2	8	4	1	10	1	-2	-9	-2	-5	-9	-1	-5

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Quadratic twists for elliptic curve 3519a1

-4	-3	5	17	-23
56304s1	3519b1	87975j1	59823b1	80937c1

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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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