Properties

Label 273600r
Number of curves $4$
Conductor $273600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("273600.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 273600r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273600.r4 273600r1 [0, 0, 0, -144300, -36002000] [2] 3538944 \(\Gamma_0(N)\)-optimal
273600.r3 273600r2 [0, 0, 0, -2736300, -1741538000] [2, 2] 7077888  
273600.r2 273600r3 [0, 0, 0, -3168300, -1154882000] [2] 14155776  
273600.r1 273600r4 [0, 0, 0, -43776300, -111482498000] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 273600r have rank \(1\).

Modular form 273600.2.a.r

sage: E.q_eigenform(10)
 
\( q - 4q^{7} - 4q^{11} - 2q^{13} - 2q^{17} + q^{19} + O(q^{20}) \)

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.