Cremona's table of elliptic curves

14400 = 2⁶ · 3² · 5²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5-	Signs for the Atkin-Lehner involutions
Class	14400dk	Isogeny class
Conductor	14400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	20480	Modular degree for the optimal curve
Δ	-864000000000 = -1 · 214 · 33 · 59	Discriminant
Eigenvalues	2- 3+ 5- -4  4  4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1500,-50000]	[a1,a2,a3,a4,a6]
Generators	[56:204:1]	Generators of the group modulo torsion
j	-432	j-invariant
L	4.5598520835833	L(r)(E,1)/r!
Ω	0.35838348267232	Real period
R	3.1808469865731	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	14400r1 3600j1 14400dl1 14400di1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 14400dk1

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
-	+	-	-4	4	4	6	-4	-4	-4	0	4	-8	0	-12	-2	-12	-2	-8	8	16	8	8	0	8

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Quadratic twists for elliptic curve 14400dk1

-4	8	-3	5
14400r1	3600j1	14400dl1	14400di1

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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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