Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("75150.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75150.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.x1 75150q2 [1, -1, 0, -4759542, -3835054634] [2] 4128768  
75150.x2 75150q1 [1, -1, 0, 161208, -228144884] [2] 2064384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 75150.2.a.x

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 4q^{7} - q^{8} - 4q^{11} + 4q^{13} - 4q^{14} + q^{16} + 4q^{19} + O(q^{20}) \)

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 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.