Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 960.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.n1 960p4 \([0, 1, 0, -865, 9503]\) \(546718898/405\) \(53084160\) \([4]\) \(512\) \(0.41598\)  
960.n2 960p3 \([0, 1, 0, -545, -5025]\) \(136835858/1875\) \(245760000\) \([2]\) \(512\) \(0.41598\)  
960.n3 960p2 \([0, 1, 0, -65, 63]\) \(470596/225\) \(14745600\) \([2, 2]\) \(256\) \(0.069403\)  
960.n4 960p1 \([0, 1, 0, 15, 15]\) \(21296/15\) \(-245760\) \([2]\) \(128\) \(-0.27717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 960.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 4 q^{7} + q^{9} + 6 q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.