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Properties

Label 308550.do
Number of curves $2$
Conductor $308550$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 308550.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308550.do1 308550do2 [1, 0, 1, -434151, -70367552] [2] 5898240  
308550.do2 308550do1 [1, 0, 1, 80099, -7629052] [2] 2949120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308550.do have rank \(0\).

Complex multiplication

The elliptic curves in class 308550.do do not have complex multiplication.

Modular form 308550.2.a.do

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{12} + 2q^{14} + q^{16} + q^{17} - q^{18} + O(q^{20}) \)

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 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.