Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("75150.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75150.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.g1 75150c2 [1, -1, 0, -126942, 16977716] [2] 460800  
75150.g2 75150c1 [1, -1, 0, -18942, -626284] [2] 230400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 75150.2.a.g

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

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.