Properties

Label 50400dx
Number of curves $4$
Conductor $50400$
CM no
Rank $2$
Graph

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

Elliptic curves in class 50400dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50400.cg3 50400dx1 \([0, 0, 0, -15825, -754000]\) \(601211584/11025\) \(8037225000000\) \([2, 2]\) \(147456\) \(1.2710\) \(\Gamma_0(N)\)-optimal
50400.cg4 50400dx2 \([0, 0, 0, -75, -2187250]\) \(-8/354375\) \(-2066715000000000\) \([2]\) \(294912\) \(1.6176\)  
50400.cg2 50400dx3 \([0, 0, 0, -32700, 1136000]\) \(82881856/36015\) \(1680315840000000\) \([4]\) \(294912\) \(1.6176\)  
50400.cg1 50400dx4 \([0, 0, 0, -252075, -48712750]\) \(303735479048/105\) \(612360000000\) \([2]\) \(294912\) \(1.6176\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50400dx have rank \(2\).

Complex multiplication

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

Modular form 50400.2.a.dx

sage: E.q_eigenform(10)
 
\(q + q^{7} - 4q^{11} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.