Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1440.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.k1 1440k3 \([0, 0, 0, -732, 7616]\) \(14526784/15\) \(44789760\) \([4]\) \(512\) \(0.38604\)  
1440.k2 1440k2 \([0, 0, 0, -507, -4354]\) \(38614472/405\) \(151165440\) \([2]\) \(512\) \(0.38604\)  
1440.k3 1440k1 \([0, 0, 0, -57, 56]\) \(438976/225\) \(10497600\) \([2, 2]\) \(256\) \(0.039465\) \(\Gamma_0(N)\)-optimal
1440.k4 1440k4 \([0, 0, 0, 213, 434]\) \(2863288/1875\) \(-699840000\) \([2]\) \(512\) \(0.38604\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1440.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4q^{11} + 2q^{13} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.