Properties

Label 5040.h
Number of curves $2$
Conductor $5040$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 5040.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5040.h1 5040bf2 \([0, 0, 0, -7248, -237508]\) \(-225637236736/1715\) \(-320060160\) \([]\) \(4320\) \(0.80685\)  
5040.h2 5040bf1 \([0, 0, 0, -48, -628]\) \(-65536/875\) \(-163296000\) \([]\) \(1440\) \(0.25755\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5040.h have rank \(1\).

Complex multiplication

The elliptic curves in class 5040.h do not have complex multiplication.

Modular form 5040.2.a.h

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.