Properties

Label 9408cm
Number of curves $2$
Conductor $9408$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 9408cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.cv2 9408cm1 \([0, 1, 0, -457, -4243]\) \(-28672/3\) \(-1106841792\) \([]\) \(3360\) \(0.47444\) \(\Gamma_0(N)\)-optimal
9408.cv1 9408cm2 \([0, 1, 0, -178817, 29068437]\) \(-1713910976512/1594323\) \(-588221108782272\) \([]\) \(43680\) \(1.7569\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9408cm have rank \(1\).

Complex multiplication

The elliptic curves in class 9408cm do not have complex multiplication.

Modular form 9408.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + q^{9} - 2 q^{11} - q^{13} + 2 q^{15} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.