Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ga1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920ga

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.eg2 73920ga1 \([0, -1, 0, -85, -923]\) \(-67108864/343035\) \(-351267840\) \([2]\) \(30720\) \(0.32407\) \(\Gamma_0(N)\)-optimal
73920.eg1 73920ga2 \([0, -1, 0, -2065, -35375]\) \(59466754384/121275\) \(1986969600\) \([2]\) \(61440\) \(0.67064\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 73920.2.a.ga

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 Cremona 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 Cremona labels.