Properties

Label 7350.r
Number of curves 2
Conductor 7350
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.r1 7350s2 [1, 1, 0, -17175, 909525] [] 31104  
7350.r2 7350s1 [1, 1, 0, 1200, 1800] [] 10368 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7350.r have rank \(1\).

Modular form 7350.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 6q^{11} - q^{12} + q^{13} + q^{16} - 3q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.