Properties

Label 73920.u
Number of curves $4$
Conductor $73920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 73920.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.u1 73920g4 \([0, -1, 0, -17031201, 27058714785]\) \(2084105208962185000201/31185000\) \(8174960640000\) \([2]\) \(2359296\) \(2.4812\)  
73920.u2 73920g3 \([0, -1, 0, -1154081, 347714721]\) \(648474704552553481/176469171805080\) \(46260334573670891520\) \([2]\) \(2359296\) \(2.4812\)  
73920.u3 73920g2 \([0, -1, 0, -1064481, 423032481]\) \(508859562767519881/62240270400\) \(16315913443737600\) \([2, 2]\) \(1179648\) \(2.1347\)  
73920.u4 73920g1 \([0, -1, 0, -60961, 7775905]\) \(-95575628340361/43812679680\) \(-11485231102033920\) \([2]\) \(589824\) \(1.7881\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 73920.u have rank \(0\).

Complex multiplication

The elliptic curves in class 73920.u do not have complex multiplication.

Modular form 73920.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{13} + q^{15} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.