Properties

Label 9450.cz
Number of curves $2$
Conductor $9450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 9450.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9450.cz1 9450ch2 \([1, -1, 1, -75980, -43170353]\) \(-17525176203/280985600\) \(-777746188800000000\) \([]\) \(155520\) \(2.1142\)  
9450.cz2 9450ch1 \([1, -1, 1, 8395, 1548397]\) \(212776173/3500000\) \(-1076414062500000\) \([]\) \(51840\) \(1.5649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9450.cz have rank \(0\).

Complex multiplication

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

Modular form 9450.2.a.cz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} + 6 q^{11} + q^{13} - q^{14} + q^{16} - 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.