Properties

Label 960.k
Number of curves $4$
Conductor $960$
CM no
Rank $0$
Graph

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

Elliptic curves in class 960.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.k1 960f3 \([0, 1, 0, -641, -6465]\) \(890277128/15\) \(491520\) \([2]\) \(256\) \(0.22238\)  
960.k2 960f4 \([0, 1, 0, -161, 639]\) \(14172488/1875\) \(61440000\) \([2]\) \(256\) \(0.22238\)  
960.k3 960f2 \([0, 1, 0, -41, -105]\) \(1906624/225\) \(921600\) \([2, 2]\) \(128\) \(-0.12420\)  
960.k4 960f1 \([0, 1, 0, 4, -6]\) \(85184/405\) \(-25920\) \([2]\) \(64\) \(-0.47077\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 960.k have rank \(0\).

Complex multiplication

The elliptic curves in class 960.k do not have complex multiplication.

Modular form 960.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - 2 q^{13} - q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.