Properties

Label 150075bj
Number of curves 2
Conductor 150075
CM no
Rank 2
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("150075.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 150075bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
150075.bj1 150075bj1 [1, -1, 0, -84042, -9356009] [2] 331776 \(\Gamma_0(N)\)-optimal
150075.bj2 150075bj2 [1, -1, 0, -78417, -10666634] [2] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 150075bj have rank \(2\).

Modular form 150075.2.a.bj

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 3q^{8} - 2q^{11} - 2q^{13} - q^{16} - 4q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.