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SageMath
E = EllipticCurve("ji1")
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)
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.