Cremona's table of elliptic curves

13804 = 2² · 7 · 17 · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 17- 29-	Signs for the Atkin-Lehner involutions
Class	13804f	Isogeny class
Conductor	13804	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	888	Modular degree for the optimal curve
Δ	-55216 = -1 · 24 · 7 · 17 · 29	Discriminant
Eigenvalues	2-  2  1 7- -3  0 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,14]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	-1048576/3451	j-invariant
L	7.2122861154566	L(r)(E,1)/r!
Ω	3.1012552265587	Real period
R	0.77520074814563	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	55216o1 124236p1 96628h1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13804f1

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	1	-	-3	0	-	-1	2	-	2	-2	6	-10	-5	-13	-8	-6	-9	-14	-8	-1	2	18	16

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Quadratic twists for elliptic curve 13804f1

-4	-3	-7
55216o1	124236p1	96628h1

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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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