Properties

Label 286650.ji
Number of curves $2$
Conductor $286650$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ji1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286650.ji

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.ji1 286650ji2 \([1, -1, 1, -507380, -124488003]\) \(10779215329/1232010\) \(1651011230206406250\) \([2]\) \(6635520\) \(2.2279\)  
286650.ji2 286650ji1 \([1, -1, 1, 43870, -9828003]\) \(6967871/35100\) \(-47037356985937500\) \([2]\) \(3317760\) \(1.8814\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 286650.ji have rank \(0\).

Complex multiplication

The elliptic curves in class 286650.ji do not have complex multiplication.

Modular form 286650.2.a.ji

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 4q^{11} - q^{13} + q^{16} - 8q^{17} + 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.