Properties

Label 1440.f
Number of curves $4$
Conductor $1440$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1440.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.f1 1440d3 \([0, 0, 0, -4323, 109402]\) \(23937672968/45\) \(16796160\) \([2]\) \(1024\) \(0.64163\)  
1440.f2 1440d2 \([0, 0, 0, -723, -5258]\) \(111980168/32805\) \(12244400640\) \([2]\) \(1024\) \(0.64163\)  
1440.f3 1440d1 \([0, 0, 0, -273, 1672]\) \(48228544/2025\) \(94478400\) \([2, 2]\) \(512\) \(0.29505\) \(\Gamma_0(N)\)-optimal
1440.f4 1440d4 \([0, 0, 0, 132, 6208]\) \(85184/5625\) \(-16796160000\) \([2]\) \(1024\) \(0.64163\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1440.f have rank \(0\).

Complex multiplication

The elliptic curves in class 1440.f do not have complex multiplication.

Modular form 1440.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} - 2 q^{13} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.