Properties

Label 9408ct
Number of curves $2$
Conductor $9408$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 9408ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.cr2 9408ct1 \([0, 1, 0, -65, 447]\) \(-2401/6\) \(-77070336\) \([]\) \(2304\) \(0.20124\) \(\Gamma_0(N)\)-optimal
9408.cr1 9408ct2 \([0, 1, 0, -9025, -345409]\) \(-6329617441/279936\) \(-3595793596416\) \([]\) \(16128\) \(1.1742\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9408ct have rank \(0\).

Complex multiplication

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

Modular form 9408.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 5 q^{11} + q^{15} + 4 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.