Cremona's table of elliptic curves

5304 = 2³ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 17-	Signs for the Atkin-Lehner involutions
Class	5304l	Isogeny class
Conductor	5304	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	7405858512 = 24 · 36 · 133 · 172	Discriminant
Eigenvalues	2- 3- -2 -2  0 13- 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-579,3222]	[a1,a2,a3,a4,a6]
Generators	[3:39:1]	Generators of the group modulo torsion
j	1343969093632/462866157	j-invariant
L	3.8871502877503	L(r)(E,1)/r!
Ω	1.2148595258679	Real period
R	0.17775947684949	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10608d1 42432d1 15912g1 68952n1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304l1

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	0	-	-	0	0	2	2	0	6	4	6	-10	-14	-10	4	-4	4	-4	2	8	-16

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Quadratic twists for elliptic curve 5304l1

-4	8	-3	13	17
10608d1	42432d1	15912g1	68952n1	90168u1

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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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