Properties

Label 235200.ox
Number of curves $2$
Conductor $235200$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ox1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200.ox

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.ox1 235200ox2 \([0, 1, 0, -1099233, 468974463]\) \(-7620530425/526848\) \(-10155317715271680000\) \([]\) \(5971968\) \(2.3980\)  
235200.ox2 235200ox1 \([0, 1, 0, 76767, 691263]\) \(2595575/1512\) \(-29144725585920000\) \([]\) \(1990656\) \(1.8487\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235200.ox have rank \(2\).

Complex multiplication

The elliptic curves in class 235200.ox do not have complex multiplication.

Modular form 235200.2.a.ox

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 6q^{11} - q^{13} - 3q^{17} - 4q^{19} + O(q^{20})\)  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 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.