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	14400do	Isogeny class
Conductor	14400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	10935000000 = 26 · 37 · 57	Discriminant
Eigenvalues	2- 3- 5+  0  4  2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4575,-119000]	[a1,a2,a3,a4,a6]
Generators	[360:6700:1]	Generators of the group modulo torsion
j	14526784/15	j-invariant
L	5.0850673832172	L(r)(E,1)/r!
Ω	0.58053539574216	Real period
R	4.3796359537358	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	14400dr1 7200h2 4800cc1 2880y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 14400do1

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

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Quadratic twists for elliptic curve 14400do1

-4	8	-3	5
14400dr1	7200h2	4800cc1	2880y1

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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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