Properties

Label 900e
Number of curves 4
Conductor 900
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("900.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 900e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
900.b3 900e1 [0, 0, 0, -300, -1375] [2] 288 \(\Gamma_0(N)\)-optimal
900.b4 900e2 [0, 0, 0, 825, -9250] [2] 576  
900.b1 900e3 [0, 0, 0, -9300, 345125] [2] 864  
900.b2 900e4 [0, 0, 0, -8175, 431750] [2] 1728  

Rank

sage: E.rank()
 

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

Modular form 900.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.