Properties

Label 443760.f
Number of curves $2$
Conductor $443760$
CM no
Rank $1$
Graph

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

Elliptic curves in class 443760.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
443760.f1 443760f1 \([0, -1, 0, -4571542176, -118669594477824]\) \(408076159454905367161/1190206406250000\) \(30817184961133906560000000000\) \([2]\) \(468357120\) \(4.3370\) \(\Gamma_0(N)\)-optimal
443760.f2 443760f2 \([0, -1, 0, -2722542176, -215546840077824]\) \(-86193969101536367161/725294740213012500\) \(-18779551213226359220122060800000\) \([2]\) \(936714240\) \(4.6835\)  

Rank

sage: E.rank()
 

The elliptic curves in class 443760.f have rank \(1\).

Complex multiplication

The elliptic curves in class 443760.f do not have complex multiplication.

Modular form 443760.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 6 q^{11} + 2 q^{13} + q^{15} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.