Cremona's table of elliptic curves

3509 = 11² · 29

Field	Data	Notes
Atkin-Lehner	11- 29+	Signs for the Atkin-Lehner involutions
Class	3509b	Isogeny class
Conductor	3509	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	17424	Modular degree for the optimal curve
Δ	5227998748709 = 118 · 293	Discriminant
Eigenvalues	-2  2 -2  1 11-  7 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-63444,-6128750]	[a1,a2,a3,a4,a6]
j	131753070592/24389	j-invariant
L	1.2032785103264	L(r)(E,1)/r!
Ω	0.30081962758159	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56144n1 31581o1 87725f1 3509e1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3509b1

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
-2	2	-2	1	-	7	-2	0	-1	+	4	6	10	0	8	-3	-7	12	8	-3	4	-10	9	-6	2

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Quadratic twists for elliptic curve 3509b1

-4	-3	5	-11	29
56144n1	31581o1	87725f1	3509e1	101761f1

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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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