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	14400b	Isogeny class
Conductor	14400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-11059200 = -1 · 214 · 33 · 52	Discriminant
Eigenvalues	2+ 3+ 5+  1  4  1 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-240,1440]	[a1,a2,a3,a4,a6]
Generators	[9:3:1]	Generators of the group modulo torsion
j	-138240	j-invariant
L	5.3393001046786	L(r)(E,1)/r!
Ω	2.2851152302743	Real period
R	1.1682780881115	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14400cu1 1800a1 14400c1 14400o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 14400b1

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
+	+	+	1	4	1	-4	-1	4	4	-5	6	-12	-5	-8	-12	8	-7	-13	-12	-6	12	-8	0	-13

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Quadratic twists for elliptic curve 14400b1

-4	8	-3	5
14400cu1	1800a1	14400c1	14400o1

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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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