Cremona's table of elliptic curves

3509 = 11² · 29

Field	Data	Notes
Atkin-Lehner	11- 29-	Signs for the Atkin-Lehner involutions
Class	3509d	Isogeny class
Conductor	3509	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	6216407549 = 118 · 29	Discriminant
Eigenvalues	2  0 -2  1 11-  3  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1331,18301]	[a1,a2,a3,a4,a6]
Generators	[242:601:8]	Generators of the group modulo torsion
j	1216512/29	j-invariant
L	5.9403154576932	L(r)(E,1)/r!
Ω	1.3387009283767	Real period
R	1.4791243589899	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	56144p1 31581i1 87725t1 3509a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3509d1

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	0	-2	1	-	3	4	4	-9	-	-4	-2	-2	-10	2	-7	-3	8	-12	-7	-4	-12	9	-6	16

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Quadratic twists for elliptic curve 3509d1

-4	-3	5	-11	29
56144p1	31581i1	87725t1	3509a1	101761h1

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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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