Properties

Label 50400.dx
Number of curves $4$
Conductor $50400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dx1")
 
E.isogeny_class()
 

Elliptic curves in class 50400.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50400.dx1 50400bn4 \([0, 0, 0, -14754675, 21813358250]\) \(60910917333827912/3255076125\) \(18983603961000000000\) \([2]\) \(1769472\) \(2.7666\)  
50400.dx2 50400bn3 \([0, 0, 0, -4770300, -3739048000]\) \(257307998572864/19456203375\) \(907748624664000000000\) \([2]\) \(1769472\) \(2.7666\)  
50400.dx3 50400bn1 \([0, 0, 0, -973425, 300827000]\) \(139927692143296/27348890625\) \(19937341265625000000\) \([2, 2]\) \(884736\) \(2.4200\) \(\Gamma_0(N)\)-optimal
50400.dx4 50400bn2 \([0, 0, 0, 2003325, 1780271750]\) \(152461584507448/322998046875\) \(-1883724609375000000000\) \([2]\) \(1769472\) \(2.7666\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50400.dx have rank \(1\).

Complex multiplication

The elliptic curves in class 50400.dx do not have complex multiplication.

Modular form 50400.2.a.dx

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.