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	3519g	Isogeny class
Conductor	3519	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	174447364573413 = 313 · 17 · 235	Discriminant
Eigenvalues	0 3-  2  1 -2 -1 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-15204,-341856]	[a1,a2,a3,a4,a6]
Generators	[-64:607:1]	Generators of the group modulo torsion
j	533174986473472/239296796397	j-invariant
L	3.3163838127585	L(r)(E,1)/r!
Ω	0.44836237245336	Real period
R	1.8491648811941	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	56304bx1 1173c1 87975q1 59823m1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3519g1

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	1	-2	-1	-	-6	+	9	2	-9	-2	-2	-4	1	4	-7	-4	3	-8	-5	11	-5	-1

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Quadratic twists for elliptic curve 3519g1

-4	-3	5	17	-23
56304bx1	1173c1	87975q1	59823m1	80937g1

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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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