Properties

Label 62400bg
Number of curves $4$
Conductor $62400$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.l3 62400bg1 [0, -1, 0, -3933, 96237] [2] 65536 \(\Gamma_0(N)\)-optimal
62400.l2 62400bg2 [0, -1, 0, -4433, 70737] [2, 2] 131072  
62400.l4 62400bg3 [0, -1, 0, 13567, 484737] [2] 262144  
62400.l1 62400bg4 [0, -1, 0, -30433, -1983263] [2] 262144  

Rank

sage: E.rank()
 

The elliptic curves in class 62400bg have rank \(2\).

Complex multiplication

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

Modular form 62400.2.a.bg

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} + q^{13} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.