Properties

Label 73920dc
Number of curves $4$
Conductor $73920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.gq4 73920dc1 \([0, 1, 0, 1455, 20943]\) \(20777545136/23059575\) \(-377808076800\) \([2]\) \(65536\) \(0.90798\) \(\Gamma_0(N)\)-optimal
73920.gq3 73920dc2 \([0, 1, 0, -8225, 189375]\) \(939083699236/300155625\) \(19670999040000\) \([2, 2]\) \(131072\) \(1.2545\)  
73920.gq2 73920dc3 \([0, 1, 0, -52225, -4465825]\) \(120186986927618/4332064275\) \(567812328652800\) \([2]\) \(262144\) \(1.6011\)  
73920.gq1 73920dc4 \([0, 1, 0, -119105, 15779103]\) \(1425631925916578/270703125\) \(35481600000000\) \([2]\) \(262144\) \(1.6011\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 73920.2.a.dc

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.