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	14400eh	Isogeny class
Conductor	14400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	58320000000 = 210 · 36 · 57	Discriminant
Eigenvalues	2- 3- 5+ -4 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1800,27000]	[a1,a2,a3,a4,a6]
Generators	[-15:225:1]	Generators of the group modulo torsion
j	55296/5	j-invariant
L	3.6860994868646	L(r)(E,1)/r!
Ω	1.084061595114	Real period
R	0.85006689275738	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	14400bp1 3600p1 1600p1 2880bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 14400eh1

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

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Quadratic twists for elliptic curve 14400eh1

-4	8	-3	5
14400bp1	3600p1	1600p1	2880bg1

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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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