Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 960.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.o1 960n3 \([0, 1, 0, -225, 1215]\) \(38614472/405\) \(13271040\) \([4]\) \(256\) \(0.18331\)  
960.o2 960n2 \([0, 1, 0, -25, -25]\) \(438976/225\) \(921600\) \([2, 2]\) \(128\) \(-0.16327\)  
960.o3 960n1 \([0, 1, 0, -20, -42]\) \(14526784/15\) \(960\) \([2]\) \(64\) \(-0.50984\) \(\Gamma_0(N)\)-optimal
960.o4 960n4 \([0, 1, 0, 95, -97]\) \(2863288/1875\) \(-61440000\) \([2]\) \(256\) \(0.18331\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 960.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 4q^{11} - 2q^{13} + q^{15} - 2q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.