Properties

Label 43120.v
Number of curves $2$
Conductor $43120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 43120.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43120.v1 43120bh2 \([0, -1, 0, -4656976, -3866605504]\) \(-23178622194826561/1610510\) \(-776089153495040\) \([]\) \(792000\) \(2.3112\)  
43120.v2 43120bh1 \([0, -1, 0, 7824, -1077824]\) \(109902239/1100000\) \(-530079334400000\) \([]\) \(158400\) \(1.5065\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43120.v have rank \(1\).

Complex multiplication

The elliptic curves in class 43120.v do not have complex multiplication.

Modular form 43120.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{9} - q^{11} + 6 q^{13} + q^{15} + 7 q^{17} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.