Properties

Label 900.d
Number of curves 2
Conductor 900
CM -3
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("900.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 900.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
900.d1 900c2 [0, 0, 0, 0, -2700] [] 432  
900.d2 900c1 [0, 0, 0, 0, 100] [3] 144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 900.d have rank \(1\).

Modular form 900.2.a.d

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

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.