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	5304k	Isogeny class
Conductor	5304	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	678912 = 210 · 3 · 13 · 17	Discriminant
Eigenvalues	2- 3+ -2 -4 -4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14144,652188]	[a1,a2,a3,a4,a6]
Generators	[73:58:1] [78:132:1]	Generators of the group modulo torsion
j	305612563186948/663	j-invariant
L	3.7129282267513	L(r)(E,1)/r!
Ω	1.8712185715884	Real period
R	3.9684602142445	Regulator
r	2	Rank of the group of rational points
S	0.99999999999984	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10608l3 42432t4 15912h3 68952h4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304k4

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	-4	-4	-	-	-4	-8	-2	-4	-6	-6	-4	-4	14	0	-10	-12	-8	-10	8	-8	6	-10

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Quadratic twists for elliptic curve 5304k4

-4	8	-3	13	17
10608l3	42432t4	15912h3	68952h4	90168be4

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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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