Properties

Label 9450.z
Number of curves $3$
Conductor $9450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 9450.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9450.z1 9450h3 \([1, -1, 0, -42567, -13650409]\) \(-3081731187/27343750\) \(-75685363769531250\) \([]\) \(139968\) \(1.9213\)  
9450.z2 9450h1 \([1, -1, 0, -4317, 110341]\) \(-21093208947/17920\) \(-7560000000\) \([]\) \(15552\) \(0.82272\) \(\Gamma_0(N)\)-optimal
9450.z3 9450h2 \([1, -1, 0, 4683, 477341]\) \(36926037/343000\) \(-105488578125000\) \([]\) \(46656\) \(1.3720\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9450.z have rank \(1\).

Complex multiplication

The elliptic curves in class 9450.z do not have complex multiplication.

Modular form 9450.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 6 q^{11} + 4 q^{13} + q^{14} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.