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Properties

Label 62400.h
Number of curves $2$
Conductor $62400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 62400.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.h1 62400by2 [0, -1, 0, -14556833, -19692938463] [2] 5898240  
62400.h2 62400by1 [0, -1, 0, -14236833, -20671178463] [2] 2949120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.h have rank \(1\).

Complex multiplication

The elliptic curves in class 62400.h do not have complex multiplication.

Modular form 62400.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} - 2q^{11} + q^{13} - 4q^{17} - 2q^{19} + O(q^{20}) \)

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.