Properties

Label 248430cu
Number of curves $2$
Conductor $248430$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.cu2 248430cu1 \([1, 0, 1, 32951, 6393272]\) \(6967871/35100\) \(-19932210746639100\) \([2]\) \(2903040\) \(1.8098\) \(\Gamma_0(N)\)-optimal
248430.cu1 248430cu2 \([1, 0, 1, -381099, 81087892]\) \(10779215329/1232010\) \(699620597207032410\) \([2]\) \(5806080\) \(2.1564\)  

Rank

sage: E.rank()
 

The elliptic curves in class 248430cu have rank \(1\).

Complex multiplication

The elliptic curves in class 248430cu do not have complex multiplication.

Modular form 248430.2.a.cu

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - q^{15} + q^{16} - 8q^{17} - q^{18} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.