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	14400h	Isogeny class
Conductor	14400	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-8640000000 = -1 · 212 · 33 · 57	Discriminant
Eigenvalues	2+ 3+ 5+ -2 -2  0  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,300,-4000]	[a1,a2,a3,a4,a6]
Generators	[20:100:1]	Generators of the group modulo torsion
j	1728/5	j-invariant
L	4.2422770487251	L(r)(E,1)/r!
Ω	0.66940407246872	Real period
R	0.79217419328655	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	14400d1 7200bc1 14400f1 2880b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 14400h1

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

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Quadratic twists for elliptic curve 14400h1

-4	8	-3	5
14400d1	7200bc1	14400f1	2880b1

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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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