Properties

Label 75150bq
Number of curves 2
Conductor 75150
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("75150.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75150bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.bj1 75150bq1 [1, -1, 1, -410, 3017] [2] 46080 \(\Gamma_0(N)\)-optimal
75150.bj2 75150bq2 [1, -1, 1, 490, 13817] [2] 92160  

Rank

sage: E.rank()
 

The elliptic curves in class 75150bq have rank \(1\).

Modular form 75150.2.a.bj

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} - 2q^{11} + 6q^{13} + q^{16} - 4q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.