Properties

Label 73920.gw
Number of curves $2$
Conductor $73920$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920.gw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.gw1 73920de2 \([0, 1, 0, -2065, 35375]\) \(59466754384/121275\) \(1986969600\) \([2]\) \(61440\) \(0.67064\)  
73920.gw2 73920de1 \([0, 1, 0, -85, 923]\) \(-67108864/343035\) \(-351267840\) \([2]\) \(30720\) \(0.32407\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 73920.gw have rank \(1\).

Complex multiplication

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

Modular form 73920.2.a.gw

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.