Properties

Label 141120.dm
Number of curves $4$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dm1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.dm1 141120dr3 \([0, 0, 0, -3175788, 2178181712]\) \(157551496201/13125\) \(295090346557440000\) \([2]\) \(3145728\) \(2.3960\)  
141120.dm2 141120dr2 \([0, 0, 0, -212268, 29037008]\) \(47045881/11025\) \(247875891108249600\) \([2, 2]\) \(1572864\) \(2.0494\)  
141120.dm3 141120dr1 \([0, 0, 0, -71148, -6920368]\) \(1771561/105\) \(2360722772459520\) \([2]\) \(786432\) \(1.7029\) \(\Gamma_0(N)\)-optimal
141120.dm4 141120dr4 \([0, 0, 0, 493332, 181164368]\) \(590589719/972405\) \(-21862653595747614720\) \([2]\) \(3145728\) \(2.3960\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141120.dm have rank \(0\).

Complex multiplication

The elliptic curves in class 141120.dm do not have complex multiplication.

Modular form 141120.2.a.dm

sage: E.q_eigenform(10)
 
\(q - q^{5} - 6 q^{13} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.