Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 960.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.h1 960d3 \([0, -1, 0, -1985, 19617]\) \(26410345352/10546875\) \(345600000000\) \([4]\) \(1536\) \(0.91221\)  
960.h2 960d2 \([0, -1, 0, -905, -9975]\) \(20034997696/455625\) \(1866240000\) \([2, 2]\) \(768\) \(0.56564\)  
960.h3 960d1 \([0, -1, 0, -900, -10098]\) \(1261112198464/675\) \(43200\) \([2]\) \(384\) \(0.21907\) \(\Gamma_0(N)\)-optimal
960.h4 960d4 \([0, -1, 0, 95, -31775]\) \(2863288/13286025\) \(-435356467200\) \([2]\) \(1536\) \(0.91221\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 960.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 4 q^{7} + q^{9} + 4 q^{11} - 6 q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.