Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 9450.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9450.h1 9450f2 \([1, -1, 0, -31767, -2171359]\) \(-11527859979/28\) \(-8611312500\) \([]\) \(23328\) \(1.1467\)  
9450.h2 9450f1 \([1, -1, 0, -267, -4859]\) \(-5000211/21952\) \(-9261000000\) \([]\) \(7776\) \(0.59736\) \(\Gamma_0(N)\)-optimal
9450.h3 9450f3 \([1, -1, 0, 2358, 118516]\) \(381790581/1835008\) \(-6967296000000\) \([]\) \(23328\) \(1.1467\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9450.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.