Properties

Label 13456f
Number of curves $2$
Conductor $13456$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 13456f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13456.i2 13456f1 \([0, -1, 0, 67000, -11109392]\) \(13651919/29696\) \(-72351225202343936\) \([]\) \(80640\) \(1.9192\) \(\Gamma_0(N)\)-optimal
13456.i1 13456f2 \([0, -1, 0, -6122760, 5872930288]\) \(-10418796526321/82044596\) \(-199893152001324302336\) \([]\) \(403200\) \(2.7240\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13456f have rank \(0\).

Complex multiplication

The elliptic curves in class 13456f do not have complex multiplication.

Modular form 13456.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2 q^{7} - 2 q^{9} - 3 q^{11} - q^{13} - q^{15} - 8 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.